$\displaystyle \int_{1}^{3} \frac{dx}{x(x+1)^2}$
I can't seem to come across a solution, any ideas?
this is how you avoid partial fractions to save time:
put $\displaystyle x=\frac1t$ and the integral becomes $\displaystyle \int_{\frac13}^1\frac t{(t+1)^2}\,dt$ now substitute $\displaystyle u=t+1$ and the integral becomes $\displaystyle \int_{\frac43}^2\frac{u-1}{u^2}\,du,$ thus the rest should be pretty easy.