simple integration problem

**yaykittyeee** · October 23rd 2009, 09:59 PM

I'm trying to review some simple integration to help me with an upcoming test. i'm stuck on this one. i need to know how to solve it with substitution.

$\int{(x^3)(\sqrt{x^2+1})dx}$

**matheagle** · October 23rd 2009, 10:13 PM

Let $u=x^2+1$ thus $du=2xdx$

and rewrite your integral as $\int x^2 x\sqrt{x^2+1}dx$

$= {1\over 2} \int x^2 \sqrt{x^2+1}(2xdx)$

$={1\over 2}\int (u-1)\sqrt{u} du$

$={1\over 2}\int (u^{3/2}-u^{1/2}) du$

Now you can integrate and replace the u's with the x's.

**yaykittyeee** · October 23rd 2009, 10:27 PM

thankyou very much

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