integral of sinx sinx(cosx) dx

Question

anonymous · Answer

substitute u = cosx, then du = -sinxdx

so it becomes the integral of -sin(u)du

= cos(u) + C

= cos(cosx) + C

anonymous · Answer

oh.. but can i also use $$\int\limits_{}^{}\sin x dx \int\limits_{}^{}six(cosx)dx$$

anonymous · Answer

what is six? a typo or a new function i haven't heard of?

anonymous · Answer

sorry for the typo. that's sin. xD

anonymous · Answer

it is not necessarily true that sin(x) = sin(cosx)

anonymous · Answer

aw.. the given is $$\int\limits_{}^{} \sin x \sin(cosx) dx$$

anonymous · Answer

yes...and that integral is cos(cosx) + C

are you aware of the chain rule?

anonymous · Answer

yes. never thought of that. ty btw. :)

anonymous · Answer

well, use the chain rule to differentiate cos(cosx) + C

what do you get?

anonymous · Answer

hbaldon, you should follow jamesm method. You can not break it up the way you did because integral has restriction on multiplication; you can break it up like that if it has a + or - between them.