230:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Integración:@0.073089:0.043661:0.176062:0.043661:0.176062:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Observamos dos integrales iguales, así que procedemos a sumarlas::@0.293660:0.135050:0.783849:0.135050:0.783849:0.119337:0.293660:0.119337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.481064:0.172633:0.494005:0.172633:0.494005:0.156920:0.481064:0.156920:0.000000:0.000000 # :@0.493913:0.173215:0.503540:0.173215:0.503540:0.155561:0.493913:0.155561:0.000000:0.000000 e cosx dx:@0.503448:0.172633:0.568827:0.172629:0.568827:0.157193:0.503448:0.157197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.511169:0.166565:0.515515:0.166565:0.515515:0.157566:0.511169:0.157566:0.000000 :@0.568802:0.172629:0.592032:0.172629:0.592032:0.156916:0.568802:0.156916:0.000000:0.000000:0.000000 5:@0.572759:0.172074:0.588093:0.172074:0.588093:0.158358:0.572759:0.158358:0.000000 e senx :@0.591958:0.172629:0.638102:0.172629:0.638102:0.157193:0.591958:0.157193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.599667:0.166565:0.604014:0.166565:0.604014:0.157566:0.599667:0.157566:0.000000 1 :@0.638065:0.172074:0.657908:0.172074:0.657908:0.158358:0.638065:0.158358:0.000000:0.000000 e cosx :@0.657816:0.172629:0.706628:0.172629:0.706628:0.157193:0.657816:0.157193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.665535:0.166565:0.669881:0.166565:0.669881:0.157566:0.665535:0.157566:0.000000 1 :@0.706583:0.172074:0.726426:0.172074:0.726426:0.158358:0.706583:0.158358:0.000000:0.000000 C.:@0.726334:0.172629:0.739496:0.172629:0.739496:0.157193:0.726334:0.157193:0.000000:0.000000 De donde:@0.293653:0.210212:0.366723:0.210212:0.366723:0.194499:0.293653:0.194499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 # :@0.293653:0.250263:0.303280:0.250263:0.303280:0.232609:0.293653:0.232609:0.000000:0.000000 e cosx dx :@0.303004:0.249680:0.371378:0.249678:0.371378:0.234243:0.303004:0.234245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.310735:0.243614:0.315082:0.243614:0.315082:0.234615:0.310735:0.234615:0.000000 5:@0.371242:0.249123:0.386575:0.249123:0.386575:0.235408:0.371242:0.235408:0.000000 :@0.386483:0.249678:0.390514:0.249678:0.390514:0.233965:0.386483:0.233965:0.000000 e senx cosx:@0.390427:0.241599:0.482256:0.241599:0.482256:0.226164:0.390427:0.226164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.398011:0.235535:0.402357:0.235535:0.402357:0.226536:0.398011:0.226536:0.000000 (:@0.402239:0.241599:0.407117:0.241599:0.407117:0.225886:0.402239:0.225886:0.000000 1:@0.437213:0.241044:0.452547:0.241044:0.452547:0.227329:0.437213:0.227329:0.000000 ):@0.482053:0.241599:0.486931:0.241599:0.486931:0.225886:0.482053:0.225886:0.000000 2:@0.434194:0.257991:0.443177:0.257991:0.443177:0.242279:0.434194:0.242279:0.000000 1:@0.487023:0.249130:0.502357:0.249130:0.502357:0.235414:0.487023:0.235414:0.000000 que era la integral que solicitaron evaluar. Un ejercicio es :@0.502265:0.249684:0.931242:0.249684:0.931242:0.233972:0.502265:0.233972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.506056:0.249684:0.515960:0.249684:0.515960:0.234249:0.506056:0.234249:0.000000 calcular la derivada del resultado de la integral para mostrar que lo trabajado es correcto.:@0.293674:0.269862:0.927008:0.269862:0.927008:0.254150:0.293674:0.254150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 6:@0.293674:0.307445:0.369456:0.307445:0.369456:0.290776:0.293674:0.290776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 # :@0.367082:0.345611:0.376709:0.345611:0.376709:0.327956:0.367082:0.327956:0.000000:0.000000 x e dx:@0.376617:0.345028:0.419141:0.345008:0.419141:0.329573:0.376617:0.329593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.394954:0.338944:0.399300:0.338944:0.399300:0.329945:0.394954:0.329945:0.000000 hagamos :@0.419085:0.345008:0.494887:0.345008:0.494887:0.329295:0.419085:0.329295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.494758:0.345008:0.504072:0.345008:0.504072:0.329573:0.494758:0.329573:0.000000 :@0.504000:0.338944:0.505931:0.338944:0.505931:0.329945:0.504000:0.329945:0.000000 5 :@0.505892:0.344453:0.525735:0.344453:0.525735:0.330738:0.505892:0.330738:0.000000:0.000000 x y dv:@0.525643:0.345008:0.563820:0.345008:0.563820:0.329573:0.525643:0.329573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.563783:0.345008:0.567814:0.345008:0.567814:0.329295:0.563783:0.329295:0.000000 5 :@0.567741:0.344453:0.587584:0.344453:0.587584:0.330738:0.567741:0.330738:0.000000:0.000000 e dx:@0.587492:0.345008:0.622646:0.345008:0.622646:0.329573:0.587492:0.329573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.598459:0.338944:0.602805:0.338944:0.602805:0.329945:0.598459:0.329945:0.000000 :@0.622594:0.338944:0.624526:0.338944:0.624526:0.329945:0.622594:0.329945:0.000000 :@0.624483:0.338944:0.626833:0.338944:0.626833:0.329784:0.624483:0.329784:0.000000 de manera que :@0.626790:0.345008:0.741559:0.345008:0.741559:0.329295:0.626790:0.329295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 du dx y v e:@0.741393:0.345008:0.849223:0.345008:0.849223:0.329573:0.741393:0.329573:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.763077:0.344453:0.778410:0.344453:0.778410:0.330738:0.763077:0.330738:0.000000 5:@0.822956:0.344453:0.838289:0.344453:0.838289:0.330738:0.822956:0.330738:0.000000 x:@0.849163:0.338944:0.853509:0.338944:0.853509:0.329945:0.849163:0.329945:0.000000 # :@0.406025:0.383169:0.415652:0.383169:0.415652:0.365515:0.406025:0.365515:0.000000:0.000000 x e dx:@0.415560:0.382587:0.458104:0.382587:0.458104:0.367152:0.415560:0.367152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.433915:0.376523:0.438261:0.376523:0.438261:0.367524:0.433915:0.367524:0.000000 :@0.458049:0.382587:0.481279:0.382587:0.481279:0.366874:0.458049:0.366874:0.000000:0.000000:0.000000 5:@0.462006:0.382032:0.477339:0.382032:0.477339:0.368317:0.462006:0.368317:0.000000 x e:@0.481205:0.382587:0.499612:0.382587:0.499612:0.367152:0.481205:0.367152:0.000000:0.000000:0.000000 x :@0.499549:0.376523:0.505784:0.376523:0.505784:0.367524:0.499549:0.367524:0.000000:0.000000 2 :@0.505749:0.382032:0.525592:0.382032:0.525592:0.368317:0.505749:0.368317:0.000000:0.000000 #:@0.525499:0.383169:0.530617:0.383169:0.530617:0.365515:0.525499:0.365515:0.000000 :@0.530525:0.382587:0.534556:0.382587:0.534556:0.366874:0.530525:0.366874:0.000000 e dx:@0.534482:0.382587:0.565037:0.382587:0.565037:0.367152:0.534482:0.367152:0.000000:0.000000:0.000000:0.000000 x :@0.542195:0.376523:0.548430:0.376523:0.548430:0.367524:0.542195:0.367524:0.000000:0.000000 :@0.564981:0.382587:0.569013:0.382587:0.569013:0.366874:0.564981:0.366874:0.000000 5 :@0.568939:0.382032:0.588782:0.382032:0.588782:0.368317:0.568939:0.368317:0.000000:0.000000 x e :@0.588690:0.382587:0.614654:0.382587:0.614654:0.367152:0.588690:0.367152:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.607034:0.376523:0.611380:0.376523:0.611380:0.367524:0.607034:0.367524:0.000000 2 1 5 2:@0.614581:0.382032:0.712295:0.382032:0.712295:0.368317:0.614581:0.368317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.634332:0.382587:0.642118:0.382587:0.642118:0.367152:0.634332:0.367152:0.000000 x :@0.642059:0.376523:0.648294:0.376523:0.648294:0.367524:0.642059:0.367524:0.000000:0.000000 :@0.663500:0.376523:0.665432:0.376523:0.665432:0.367524:0.663500:0.367524:0.000000 C :@0.665393:0.382587:0.697035:0.382587:0.697035:0.367152:0.665393:0.367152:0.000000:0.000000:0.000000:0.000000 (:@0.712203:0.382587:0.736301:0.382587:0.736301:0.366874:0.712203:0.366874:0.000000:0.000000:0.000000 e x:@0.716160:0.382587:0.743682:0.382587:0.743682:0.367152:0.716160:0.367152:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.723876:0.376523:0.728222:0.376523:0.728222:0.367524:0.723876:0.367524:0.000000 :@0.743617:0.376523:0.747437:0.376523:0.747437:0.367524:0.743617:0.367524:0.000000:0.000000 2:@0.747402:0.382032:0.762736:0.382032:0.762736:0.368317:0.747402:0.368317:0.000000 :@0.762643:0.376523:0.764575:0.376523:0.764575:0.367524:0.762643:0.367524:0.000000 1) :@0.764536:0.382587:0.801461:0.382587:0.801461:0.366874:0.764536:0.366874:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.782189:0.382032:0.797522:0.382032:0.797522:0.368317:0.782189:0.368317:0.000000 C.:@0.801387:0.382587:0.814549:0.382587:0.814549:0.367152:0.801387:0.367152:0.000000:0.000000 Ejemplo 7:@0.293679:0.420170:0.369461:0.420170:0.369461:0.403500:0.293679:0.403500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Finalmente, veamos un ejemplo interesante debido a su manejo y que necesita de :@0.293679:0.457753:0.931041:0.457753:0.931041:0.442040:0.293679:0.442040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 integración por partes.:@0.293679:0.476031:0.457857:0.476031:0.457857:0.460318:0.293679:0.460318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 # :@0.293679:0.528688:0.303306:0.528688:0.303306:0.511034:0.293679:0.511034:0.000000:0.000000 lnx dx:@0.303213:0.528106:0.343617:0.528106:0.343617:0.512671:0.303213:0.512671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 hacemos :@0.343581:0.528106:0.418148:0.528106:0.418148:0.512393:0.343581:0.512393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u :@0.418020:0.528106:0.430573:0.528106:0.430573:0.512671:0.418020:0.512671:0.000000:0.000000 5 :@0.430518:0.527551:0.450361:0.527551:0.450361:0.513836:0.430518:0.513836:0.000000:0.000000 lnx y dv:@0.450269:0.528106:0.501588:0.528106:0.501588:0.512671:0.450269:0.512671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.501570:0.528106:0.505601:0.528106:0.505601:0.512393:0.501570:0.512393:0.000000 5 :@0.505528:0.527551:0.525371:0.527551:0.525371:0.513836:0.505528:0.513836:0.000000:0.000000 dx:@0.525279:0.528106:0.541919:0.528106:0.541919:0.512671:0.525279:0.512671:0.000000:0.000000 :@0.541830:0.522041:0.543762:0.522041:0.543762:0.513042:0.541830:0.513042:0.000000 :@0.543719:0.522041:0.546069:0.522041:0.546069:0.512880:0.543719:0.512880:0.000000 de manera que :@0.546027:0.528105:0.660796:0.528105:0.660796:0.512392:0.546027:0.512392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 du :@0.660630:0.528105:0.700869:0.528105:0.700869:0.512669:0.660630:0.512669:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.682314:0.527550:0.697647:0.527550:0.697647:0.513834:0.682314:0.513834:0.000000 1:@0.705628:0.520918:0.714611:0.520918:0.714611:0.505206:0.705628:0.505206:0.000000 x:@0.706383:0.537311:0.713837:0.537311:0.713837:0.521875:0.706383:0.521875:0.000000 :@0.719341:0.527547:0.723943:0.527547:0.723943:0.513832:0.719341:0.513832:0.000000 dx y v x:@0.723851:0.528102:0.791185:0.528102:0.791185:0.512667:0.723851:0.512667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.765249:0.527547:0.780582:0.527547:0.780582:0.513832:0.765249:0.513832:0.000000 :@0.791185:0.528102:0.795216:0.528102:0.795216:0.512389:0.791185:0.512389:0.000000 # :@0.293655:0.580760:0.303282:0.580760:0.303282:0.563105:0.293655:0.563105:0.000000:0.000000 lnx dx:@0.303190:0.580177:0.343594:0.580177:0.343594:0.564742:0.303190:0.564742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.343557:0.580177:0.347588:0.580177:0.347588:0.564465:0.343557:0.564465:0.000000 5 :@0.347515:0.579622:0.367358:0.579622:0.367358:0.565907:0.347515:0.565907:0.000000:0.000000 x lnx :@0.367266:0.580177:0.401724:0.580177:0.401724:0.564742:0.367266:0.564742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.401687:0.579622:0.431065:0.579622:0.431065:0.565907:0.401687:0.565907:0.000000:0.000000:0.000000:0.000000 #:@0.421438:0.580760:0.426555:0.580760:0.426555:0.563105:0.421438:0.563105:0.000000 x dx:@0.430973:0.580177:0.472880:0.580180:0.472880:0.564744:0.430973:0.564742:0.000000:0.000000:0.000000:0.000000 :@0.438373:0.574118:0.440305:0.574118:0.440305:0.565120:0.438373:0.565120:0.000000 :@0.440262:0.574118:0.442612:0.574118:0.442612:0.564958:0.440262:0.564958:0.000000 1:@0.442710:0.572996:0.451693:0.572996:0.451693:0.557283:0.442710:0.557283:0.000000 x:@0.443465:0.589388:0.450920:0.589388:0.450920:0.573953:0.443465:0.573953:0.000000 :@0.451730:0.579625:0.456332:0.579625:0.456332:0.565909:0.451730:0.565909:0.000000 :@0.472825:0.580180:0.496055:0.580180:0.496055:0.564467:0.472825:0.564467:0.000000:0.000000:0.000000 5:@0.476782:0.579625:0.492115:0.579625:0.492115:0.565909:0.476782:0.565909:0.000000 x lnx :@0.495981:0.580180:0.530439:0.580180:0.530439:0.564744:0.495981:0.564744:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.530403:0.579625:0.593498:0.579628:0.593498:0.565912:0.530403:0.565909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.550153:0.580762:0.555271:0.580762:0.555271:0.563108:0.550153:0.563108:0.000000 dx:@0.559688:0.580180:0.576329:0.580180:0.576329:0.564744:0.559688:0.564744:0.000000:0.000000 :@0.576270:0.574118:0.578202:0.574118:0.578202:0.565120:0.576270:0.565120:0.000000 :@0.593406:0.580182:0.597437:0.580182:0.597437:0.564470:0.593406:0.564470:0.000000 x lnx :@0.597363:0.580182:0.631821:0.580182:0.631821:0.564747:0.597363:0.564747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 1 5:@0.631785:0.579628:0.709077:0.579628:0.709077:0.565912:0.631785:0.565912:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x C x lnx :@0.651536:0.580182:0.766783:0.580182:0.766783:0.564747:0.651536:0.564747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.719624:0.580182:0.724502:0.580182:0.724502:0.564470:0.719624:0.564470:0.000000 2:@0.748229:0.579628:0.763562:0.579628:0.763562:0.565912:0.748229:0.565912:0.000000 1) :@0.766710:0.580182:0.803635:0.580182:0.803635:0.564470:0.766710:0.564470:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.784362:0.579628:0.799696:0.579628:0.799696:0.565912:0.784362:0.565912:0.000000 C.:@0.803561:0.580182:0.816722:0.580182:0.816722:0.564747:0.803561:0.564747:0.000000:0.000000 3.3 Integración por sustitución trigonométrica:@0.293680:0.617765:0.656566:0.617765:0.656566:0.600818:0.293680:0.600818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aquí utilizaremos algunas de las identidades trigonométricas trabajadas en grado :@0.293680:0.655348:0.931041:0.655348:0.931041:0.639635:0.293680:0.639635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 décimo para realizar las sustituciones que faciliten la solución de la integral.:@0.293680:0.673626:0.837257:0.673626:0.837257:0.657913:0.293680:0.657913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 8:@0.293680:0.711209:0.369463:0.711209:0.369463:0.694539:0.293680:0.694539:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Evaluar :@0.293680:0.748792:0.358768:0.748792:0.358768:0.733079:0.293680:0.733079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.349712:0.749374:0.354829:0.749374:0.354829:0.731720:0.349712:0.731720:0.000000 ct g x csc x dx:@0.358695:0.748792:0.459315:0.748779:0.459315:0.733344:0.358695:0.733356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.384005:0.742715:0.389241:0.742715:0.389241:0.733555:0.384005:0.733555:0.000000 4 :@0.424561:0.742715:0.432105:0.742715:0.432105:0.733555:0.424561:0.733555:0.000000:0.000000 Utilicemos la identidad trigonométrica :@0.293668:0.786362:0.577818:0.786362:0.577818:0.770649:0.293668:0.770649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 csc x ctg x :@0.577490:0.786362:0.686506:0.786358:0.686506:0.770923:0.577490:0.770927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.598965:0.780294:0.604201:0.780294:0.604201:0.771134:0.598965:0.771134:0.000000 2:@0.614793:0.785803:0.630126:0.785803:0.630126:0.772088:0.614793:0.772088:0.000000 2:@0.652121:0.780294:0.657358:0.780294:0.657358:0.771134:0.652121:0.771134:0.000000 5:@0.667952:0.785803:0.683285:0.785803:0.683285:0.772088:0.667952:0.772088:0.000000 1:@0.686432:0.786358:0.695415:0.786358:0.695415:0.770646:0.686432:0.770646:0.000000 #:@0.437750:0.824523:0.442868:0.824523:0.442868:0.806869:0.437750:0.806869:0.000000 :@0.442776:0.823941:0.446807:0.823941:0.446807:0.808228:0.442776:0.808228:0.000000 ctg x csc x csc x dx ctg x :@0.446733:0.823941:0.648100:0.823937:0.648100:0.808502:0.446733:0.808506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.468822:0.817873:0.474059:0.817873:0.474059:0.808713:0.468822:0.808713:0.000000 2:@0.506132:0.817873:0.511369:0.817873:0.511369:0.808713:0.506132:0.808713:0.000000 2:@0.543442:0.817873:0.548678:0.817873:0.548678:0.808713:0.543442:0.808713:0.000000 :@0.556012:0.823382:0.560614:0.823382:0.560614:0.809667:0.556012:0.809667:0.000000 :@0.577110:0.817873:0.579460:0.817873:0.579460:0.808713:0.577110:0.808713:0.000000 5:@0.582652:0.823382:0.597986:0.823382:0.597986:0.809667:0.582652:0.809667:0.000000 #:@0.601133:0.824520:0.606250:0.824520:0.606250:0.806865:0.601133:0.806865:0.000000 :@0.606158:0.823937:0.610190:0.823937:0.610190:0.808225:0.606158:0.808225:0.000000 6:@0.632216:0.817873:0.637453:0.817873:0.637453:0.808713:0.632216:0.808713:0.000000 (1 :@0.648045:0.823937:0.684970:0.823937:0.684970:0.808225:0.648045:0.808225:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.665697:0.823382:0.681031:0.823382:0.681031:0.809667:0.665697:0.809667:0.000000 ctg x csc x dx:@0.684896:0.823937:0.782803:0.823937:0.782803:0.808502:0.684896:0.808502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.706975:0.817873:0.712212:0.817873:0.712212:0.808713:0.706975:0.808713:0.000000 ):@0.719545:0.823937:0.724423:0.823937:0.724423:0.808225:0.719545:0.808225:0.000000 2:@0.749081:0.817873:0.754318:0.817873:0.754318:0.808713:0.749081:0.808713:0.000000 :@0.761653:0.823382:0.766255:0.823382:0.766255:0.809667:0.761653:0.809667:0.000000 :@0.782816:0.817873:0.785166:0.817873:0.785166:0.808713:0.782816:0.808713:0.000000 Hacemos la sustitución :@0.293660:0.861516:0.478469:0.861516:0.478469:0.845804:0.293660:0.845804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.465197:0.861516:0.474511:0.861516:0.474511:0.846081:0.465197:0.846081:0.000000 5 :@0.478395:0.860962:0.498238:0.860962:0.498238:0.847246:0.478395:0.847246:0.000000:0.000000 ctgx du csc xdx :@0.498146:0.861516:0.643179:0.861516:0.643179:0.846081:0.498146:0.846081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.552558:0.860962:0.586372:0.860962:0.586372:0.847246:0.552558:0.847246:0.000000:0.000000:0.000000 2:@0.607775:0.855452:0.613012:0.855452:0.613012:0.846292:0.607775:0.846292:0.000000 es decir:@0.643135:0.861516:0.698872:0.861516:0.698872:0.845804:0.643135:0.845804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 du csc xdx:@0.698744:0.861516:0.811059:0.861516:0.811059:0.846081:0.698744:0.846081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.701983:0.860962:0.717316:0.860962:0.717316:0.847246:0.701983:0.847246:0.000000 5:@0.742166:0.860962:0.757499:0.860962:0.757499:0.847246:0.742166:0.847246:0.000000 2:@0.782135:0.855452:0.787372:0.855452:0.787372:0.846292:0.782135:0.846292:0.000000 #:@0.326149:0.914174:0.331266:0.914174:0.331266:0.896520:0.326149:0.896520:0.000000 (1 )(:@0.331174:0.913591:0.410516:0.913594:0.410516:0.897882:0.331174:0.897879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.335132:0.913591:0.344446:0.913591:0.344446:0.898156:0.335132:0.898156:0.000000 6:@0.344365:0.907531:0.349602:0.907531:0.349602:0.898370:0.344365:0.898370:0.000000 1:@0.367207:0.913040:0.382540:0.913040:0.382540:0.899324:0.367207:0.899324:0.000000 u:@0.386406:0.913594:0.395720:0.913594:0.395720:0.898159:0.386406:0.898159:0.000000 2:@0.395645:0.907531:0.400882:0.907531:0.400882:0.898370:0.395645:0.898370:0.000000 2:@0.410424:0.913040:0.425757:0.913040:0.425757:0.899324:0.410424:0.899324:0.000000 dx u :@0.425665:0.913594:0.516303:0.913594:0.516303:0.898159:0.425665:0.898159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ):@0.442250:0.913594:0.447128:0.913594:0.447128:0.897882:0.442250:0.897882:0.000000 :@0.447049:0.907531:0.449400:0.907531:0.449400:0.898370:0.447049:0.898370:0.000000 5 2:@0.452592:0.913040:0.486406:0.913040:0.486406:0.899324:0.452592:0.899324:0.000000:0.000000:0.000000 #:@0.489553:0.914177:0.494671:0.914177:0.494671:0.896523:0.489553:0.896523:0.000000 :@0.494579:0.913594:0.498610:0.913594:0.498610:0.897882:0.494579:0.897882:0.000000 6:@0.507798:0.907531:0.513035:0.907531:0.513035:0.898370:0.507798:0.898370:0.000000 1:@0.516229:0.913040:0.531562:0.913040:0.531562:0.899324:0.516229:0.899324:0.000000 ):@0.531470:0.913594:0.554744:0.913594:0.554744:0.897882:0.531470:0.897882:0.000000:0.000000:0.000000 u du:@0.535428:0.913594:0.576402:0.913594:0.576402:0.898159:0.535428:0.898159:0.000000:0.000000:0.000000:0.000000:0.000000 8:@0.544675:0.907531:0.549912:0.907531:0.549912:0.898370:0.544675:0.898370:0.000000 :@0.576350:0.907531:0.578700:0.907531:0.578700:0.898370:0.576350:0.898370:0.000000 52:@0.578653:0.913040:0.611532:0.913040:0.611532:0.899324:0.578653:0.899324:0.000000:0.000000 :@0.593894:0.907531:0.596244:0.907531:0.596244:0.898370:0.593894:0.898370:0.000000 :@0.611440:0.907531:0.621002:0.907531:0.621002:0.898370:0.611440:0.898370:0.000000:0.000000:0.000000 1:@0.613963:0.918681:0.618049:0.918681:0.618049:0.895399:0.613963:0.895399:0.000000 u:@0.620996:0.906409:0.630310:0.906409:0.630310:0.890974:0.620996:0.890974:0.000000 7:@0.630108:0.900345:0.635345:0.900345:0.635345:0.891184:0.630108:0.891184:0.000000 7:@0.623680:0.922799:0.632663:0.922799:0.632663:0.907086:0.623680:0.907086:0.000000 1 :@0.635295:0.913035:0.659648:0.913035:0.659648:0.899320:0.635295:0.899320:0.000000:0.000000:0.000000 u:@0.659985:0.906409:0.669299:0.906409:0.669299:0.890974:0.659985:0.890974:0.000000 9:@0.669096:0.900345:0.674333:0.900345:0.674333:0.891184:0.669096:0.891184:0.000000 9:@0.662667:0.922799:0.671650:0.922799:0.671650:0.907086:0.662667:0.907086:0.000000 2:@0.674889:0.917614:0.678976:0.917614:0.678976:0.894332:0.674889:0.894332:0.000000 1 5 2:@0.679597:0.913040:0.750759:0.913040:0.750759:0.899324:0.679597:0.899324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C :@0.703857:0.913594:0.735499:0.913594:0.735499:0.898159:0.703857:0.898159:0.000000:0.000000:0.000000:0.000000 :@0.750670:0.907531:0.760234:0.907531:0.760234:0.898370:0.750670:0.898370:0.000000:0.000000:0.000000 1:@0.753196:0.918681:0.757282:0.918681:0.757282:0.895399:0.753196:0.895399:0.000000 ctg x:@0.760401:0.906409:0.794659:0.906409:0.794659:0.890974:0.760401:0.890974:0.000000:0.000000:0.000000:0.000000:0.000000 7:@0.782085:0.900345:0.787322:0.900345:0.787322:0.891184:0.782085:0.891184:0.000000 7:@0.773030:0.922801:0.782013:0.922801:0.782013:0.907088:0.773030:0.907088:0.000000 1 :@0.794769:0.913038:0.819122:0.913038:0.819122:0.899322:0.794769:0.899322:0.000000:0.000000:0.000000 ctg x:@0.819042:0.906409:0.853062:0.906409:0.853062:0.890974:0.819042:0.890974:0.000000:0.000000:0.000000:0.000000:0.000000 9:@0.840533:0.900345:0.845770:0.900345:0.845770:0.891184:0.840533:0.891184:0.000000 9:@0.831562:0.922801:0.840545:0.922801:0.840545:0.907088:0.831562:0.907088:0.000000 2:@0.853190:0.917614:0.857277:0.917614:0.857277:0.894332:0.853190:0.894332:0.000000 :@0.857898:0.913040:0.862499:0.913040:0.862499:0.899324:0.857898:0.899324:0.000000 1 :@0.862407:0.912907:0.881349:0.912907:0.881349:0.899815:0.862407:0.899815:0.000000:0.000000 C.:@0.881260:0.913594:0.894421:0.913594:0.894421:0.898159:0.881260:0.898159:0.000000:0.000000 Para calcular áreas y :@0.082576:0.202677:0.224739:0.202677:0.224739:0.187679:0.082576:0.187679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 volúmenes de secciones :@0.082576:0.218563:0.258088:0.218563:0.258088:0.203564:0.082576:0.203564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 curvas en estructuras. :@0.082576:0.234448:0.237794:0.234448:0.237794:0.219450:0.082576:0.219450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Por ejemplo, al diseñar :@0.082576:0.250334:0.244155:0.250334:0.244155:0.235335:0.082576:0.235335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 arcos o túneles circula-:@0.082576:0.266219:0.242275:0.266219:0.242275:0.251220:0.082576:0.251220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 res, es común encontrar :@0.082576:0.282104:0.254609:0.282104:0.254609:0.267106:0.082576:0.267106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 integrales que involu-:@0.082576:0.297990:0.234333:0.297990:0.234333:0.282991:0.082576:0.282991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cran raíces cuadradas :@0.082576:0.313875:0.236230:0.313875:0.236230:0.298877:0.082576:0.298877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que representan distan-:@0.082576:0.329760:0.249533:0.329760:0.249533:0.314762:0.082576:0.314762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cias o alturas en fun-:@0.082576:0.345646:0.226057:0.345646:0.226057:0.330647:0.082576:0.330647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ción de un ángulo. La :@0.082576:0.361531:0.236863:0.361531:0.236863:0.346533:0.082576:0.346533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sustitución trigonomé-:@0.082576:0.377417:0.243680:0.377417:0.243680:0.362418:0.082576:0.362418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trica ayuda a simplificar :@0.082576:0.393302:0.249848:0.393302:0.249848:0.378304:0.082576:0.378304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estas integrales y facilita :@0.082576:0.409187:0.253941:0.409187:0.253941:0.394189:0.082576:0.394189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el cálculo de volúme-:@0.082576:0.425073:0.233050:0.425073:0.233050:0.410074:0.082576:0.410074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 nes de excavación o de :@0.082576:0.440958:0.249582:0.440958:0.249582:0.425960:0.082576:0.425960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 material necesario para :@0.082576:0.456844:0.249001:0.456844:0.249001:0.441845:0.082576:0.441845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el refuerzo estructural.:@0.082576:0.472729:0.237689:0.472729:0.237689:0.457730:0.082576:0.457730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinaria :@0.078581:0.141152:0.201990:0.141152:0.201990:0.125745:0.078581:0.125745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática :@0.078581:0.156281:0.164074:0.156281:0.164074:0.141996:0.078581:0.141996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e ingeniería civil:@0.078581:0.171410:0.184868:0.171410:0.184868:0.157125:0.078581:0.157125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t.ly/v0BDu:@0.105050:0.936466:0.180023:0.936466:0.180023:0.920754:0.105050:0.920754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Demostración :@0.080204:0.798697:0.193000:0.798697:0.193000:0.781750:0.080204:0.781750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de una identidad :@0.080204:0.810041:0.214871:0.810041:0.214871:0.793094:0.080204:0.793094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trigonométrica:@0.080204:0.821385:0.196869:0.821385:0.196869:0.804439:0.080204:0.804439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000