Integration by parts: Integrate tan^-1x dx

[Simon1268]

Just doing a bit of practice and got stuck on this one

Integrate tan^-1x dx

ok so by parts I've got

f=tan^-1x
f'=1/(1+x²)
g'=1
g=x

giving

xtan^-1x - intergral of (x/(1+x²) dx

Apparently x(1+x²) integrates directly to (1/2) ln|1+x²|

Now I must be missing a trick here cos I can't see it using a list of standard integrals. I can differentiate the answer using the composite rule back nicely to the intergrand but I just cant see it.

Thanks

 

[tkhunny]

That's pretty good. Have you considered a substitution?

Note: No need for absolute values. 1 + x^2 > 0 - Awesome that you included them. Many forget. Feel free to discard them when they are not needed.

Note: Don't forget your constant of integration. Many forget that, too. It's important.