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Topic: integration by substitution
Replies: 2   Last Post: Jun 7, 2012 7:53 AM

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Posts: 14
From: here
Registered: 6/5/12
Re: integration by substitution
Posted: Jun 5, 2012 8:14 PM
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You can separate x^3 into x^2(x) so your integral
int x^3(1- x^2)^(1/2)dx= int x^2(1- x^2)^(1/2)(xdx)

Now let u= 1-x^2 so that du= -2xdx and -(1/2)du= xdx. Also x^2= 1- u so your integral becomes int (1- u)u^(1/2)(-1/2)du= -(1/2)\int (u^(1/2)- u^(3/2))du.

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