# How do I start this problem?

• September 16th 2009, 06:52 PM
dude487
How do I start this problem?
\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
• September 16th 2009, 07:21 PM
Krizalid
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.
• September 16th 2009, 07:59 PM
Calculus26
is the pblm xarctan(x)/sqrt(x^2+1)

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

if the pblm is xarctan(sqrt(x))

See attachment