TITLE: How is this definite integral solved: $\int_{-\sqrt3}^{\sqrt3}{e^x\over(e^x+1)(x^2+1)}dx $?
QUESTION [5 upvotes]: $$\int_{-\sqrt3}^{\sqrt3}{e^x\over(e^x+1)(x^2+1)}dx $$
Tried partially integrating, had no luck.. Any thoughts?

REPLY [5 votes]: There is another way to solve. Let
$$ A=\int_{-\sqrt3}^{\sqrt3}{e^x\over(e^x+1)(x^2+1)}dx, B=\int_{-\sqrt3}^{\sqrt3}{1\over(e^x+1)(x^2+1)}dx. $$ 
Clearly
$$ A+B=\int_{-\sqrt3}^{\sqrt3}\frac{1}{x^2+1}=2\frac{\pi}{3}.$$
Changing variable $x\to -x$, it is easy to get $A=B$. Thus
$$ A=\frac{\pi}{3}. $$