evaluating integrals

**AnnaBee123** · May 10th 2009, 11:44 AM

I have two integrals I havent been able to evaluate from my last homework assignment. here they are. would some one be able to show how these two are done?

integral sin^(2)x cos^(5)x dx

integral x ln(1+x) dx

**skeeter** · May 10th 2009, 11:51 AM

Originally Posted by AnnaBee123

integral sin^(2)x cos^(5)x dx

$\sin^2{x}\cos^5{x} = \sin^2{x}(1-\sin^2{x})^2 \cos{x}$

expand the factors with sine, then let $u = \sin{x}$

integral x ln(1+x) dx

integration by parts ...

$u = \ln(1+x)$ , $dv = x \, dx$

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