Originally Posted by

**Jones** Hello,

I'm trying to integrate the following:

$\displaystyle \int sin^4 x\cdot cos^5 x$

rewrite:

$\displaystyle sin^4x(cosx\cdot cos^4 x)$

$\displaystyle cos^2 x = (1-sin^2x)$

$\displaystyle cos^4 x = (1-sin^2x)^2 = 1-2sin^2x+sin^4x$

multiply together:

$\displaystyle sin^4x-2sin^6x+sin^8x \cdot cosx$

let u = sin x, du = cos x

we have $\displaystyle u^4-2u^6+u^8 du$

My question is, the derivative of u is cos x

But we have 3 u terms. Aren't you getting a ŽduŽ for every u term?