How do I start this problem?

**dude487** · September 16th 2009, 06:52 PM

\int \frac{xtan^-1 } {sqrt 1+x^2} dx

I'm pretty sure I have to find uv, v, du and u, but I'm having some trouble with it. Tried trigonometric substitution but it doesn't seem to be working. any help would be appreciated

hope the problem's understandable

**Krizalid** · September 16th 2009, 07:21 PM

Yes, integration by parts will make this easier, we have

$\int{\frac{x\arctan x}{\sqrt{1+x^{2}}}\,dx}=\sqrt{1+x^{2}}\arctan x-\int{\frac{\sqrt{1+x^{2}}}{1+x^{2}}\,dx},$ and as for the computation for last integral we have $\int{\frac{\sqrt{1+x^{2}}}{1+x^{2}}\,dx}=\int{\fra c{dx}{\sqrt{1+x^{2}}}},$ and put $t=x+\sqrt{x^2+1}$ to finish the problem.

**Calculus26** · September 16th 2009, 07:59 PM

is the pblm xarctan(x)/sqrt(x^2+1)

0r xarctan(sqrt(x^2+1)) ?

if the pblm is xarctan(sqrt(x))

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