1. ## Integral

I need help with an Integral.

It is:

2(sin2x)^3... so I set u to 2x and du to 2 so this would make he integral of

du(sinu)^3... now I'm stuck

Thanks

2. Originally Posted by alex.caine
I need help with an Integral.

It is:

2(sin2x)^3... so I set u to 2x and du to 2 so this would make he integral of

du(sinu)^3... now I'm stuck

Thanks
$\int\sin^3u\,du$

$=\int\sin u\sin^2 u\,du$

$=\int\sin u(1-\cos^2u)\,du$

$=\int\sin u\,du-\int\sin u\cos^2u\,du$

Can you handle it from here?

3. $\int 2\sin^3(2x)dx = \int 2\sin(2x)(1-\cos^2(2x))$
$=\int2\sin(2x)-2\sin(2x)\cos^2(2x)$
$=-\cos(2x)-\cos^3(2x)$ (differentiate to check)

Works for all odd-powered trig integrals.