## anonymous 5 years ago How do I solve "integral [ sin(x) * cos(x) ] dx" ?

1. anonymous

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

2. anonymous

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

3. anonymous

is it possible to do it with partial integration?

4. anonymous

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) ..

5. anonymous

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.

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