Integral

**alex.caine** · March 10th 2009, 09:35 AM

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

**Reckoner** · March 10th 2009, 10:00 AM

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?

**Thomas154321** · March 10th 2009, 10:01 AM

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

Works for all odd-powered trig integrals.

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