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.

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

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- Oct 23rd 2009, 09:59 PMyaykittyeeesimple integration problem
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.

$\displaystyle \int{(x^3)(\sqrt{x^2+1})dx}$ - Oct 23rd 2009, 10:13 PMmatheagle
Let $\displaystyle u=x^2+1$ thus $\displaystyle du=2xdx$

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

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

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

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

Now you can integrate and replace the u's with the x's. - Oct 23rd 2009, 10:27 PMyaykittyeee
thankyou very much