How do I solve "integral [ sin(x) * cos(x) ] dx" ?

Question

anonymous · Answer

$$\int\limits_{?}^{?} [ \sin(x) * \cos(x) ] dx$$

anonymous · Answer

Try u-substitution. Let u = sin(x). This means that du=cos(x)dx. Now it's ready to substitute back in the original equation to get:
$$\int\limits_{?}^{?}udu$$
This integral is (1/2)u^2 + c. Substituting back in for x you get:
(1/2)sin^2(x) + c

anonymous · Answer

is it possible to do it with partial integration?

anonymous · Answer

also ... how do i know i have to do substitution? i mean ... i can easily get the antiderivative of both sin(x) and cos(x) ..

anonymous · Answer

but getting an antiderivative of cos(x)sin(x) is different. You might be able to get it using parts but it would be more work than it's worth. When ever I do integrals I always ask myself first if I know an antiderivative and if I don't I move to u-sub because I find u-sub to be the next easiest.