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#### karush

##### Well-known member

- Jan 31, 2012

- 3,002

**substitution**

*U*$\displaystyle

\int \sin^6(x)\cos^3(x)

$

since \(\displaystyle \cos^3(x)\) has an odd power then

$\displaystyle

\int \sin^6(x)\left(1-\sin^2(x)\right)\cos(x) dx

$

then substitute \(\displaystyle u=\sin(x)\) and \(\displaystyle du=cos(x)dx\)

$

\int u^6 \left(1-u^2\right) du

$

so if ok so far