Expert: Ahmed Salami - 7/25/2009

Question
can you help me integrate (arctan x)/1+x^2?
I would be most pleased,


Answer
Hi Dave,
To solve ∫(arctan x)/1+x² dx, you dont even need to integrate by parts.
Just a change of variable is needed. We know that d/dx [arctan x] = 1/1+x²
So, let v = arctan x
dv/dx = 1/1+x²
dx = (1+x²)dv
Substituting back,
∫(arctan x)/1+x² dx = ∫v/1+x² . (1+x²)dv
                   = ∫v.dv
                   = v²/2 + c
                   = (arctan x)²/2 + c

You can always get back to me.

Regards