How do you find the indefinite integral of $int sin^3xcosxdxdx$ ?

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Answer 1 · 2016-11-09T23:14:55

$int sin^3xcosxdx = 1/4sin^4x +C$

Let $u=sinx$
Then, $(du)/dx = cosx => int ...du = int ...cosxdx$

Substituting into the integral gives:

$int sin^3xcosxdx = int u^3du$
$:. int sin^3xcosxdx = 1/4u^4 +C$
$:. int sin^3xcosxdx = 1/4sin^4x +C$

How do you find the indefinite integral of int sin^3xcosxdxdxint sin^3xcosxdxdx?