Respuestas

2012-09-12T01:13:40+02:00

ʃsen2x/cos^4 x+sen^4 x dx

=ʃ(2senxcosx/cos^4x+sen^4x)dx

=ʃ(2senx/cos^3x+sen^4x)dx

u=cosx

du=-senxdx

=ʃ(-2du/u^3)+ʃ(sen^4x)dx

=-2(u^-2)/-2+ʃ(1-sen^2x)^2dx

=u^-2+ʃ(1-(1-cos2x)/2)^2dx

=cosx^-2+ʃ(cos2x/2+1/2)^2dx

=cosx^-2+ʃ(cos^2(2x)/4+cos2x/2+1/4)dx

=cosx^-2+ʃ(1+cos4x)/8+cos2x/2+1/4)dx

=cosx^-2+ʃ(3/8+cos4x/8+cos2x/2)dx

=cosx^-2+3x/8+sen4x/32-sen2x/4+c