Hi!

Problem:$\displaystyle \int_{1}^{2} \frac{x\cdot ln(x)}{(1+x^{2})^{2}} \; dx $

What is the smartest approach?

I tried letting $\displaystyle (1+x^{2})=t $ , because then I found that $\displaystyle x = \sqrt{t-1} \mbox{ and } dx=\frac{dt}{2\sqrt{t-1}} $ , so that square root expression would cancel which is nice.

I got stuck somewhere along the road though.

I landed first at: $\displaystyle \frac{1}{4} \int_{2}^{5} \frac{ln(t-1)}{t^{2}} \; dt $ and from here I tried using integration by parts first, integrating $\displaystyle \frac{1}{t^{2}} $ , but this might be wrong approach.

Thx!