Finding value of $\displaystyle \int^\infty_{-\infty}\frac{e^{2x}-e^x}{x(e^{2x}+1)(e^x+1)} \, dx$
Attempt: Let $\displaystyle I = \int^\infty_{-\infty}\frac{e^{2x}-e^x}{x(e^{2x}+1)(e^x+1)} \, dx = 2\int^\infty_0 \frac{e^{2x}-e^x}{x(e^{2x}+1)(e^x+1)} \, dx$
So $$I = 2\int^\infty_0 \bigg(\frac{1}{e^x+1}-\frac 1 {e^{2x}+1}\bigg)\frac 1 x \, dx = 2\int_0^\infty \frac 1 {(e^x+1)x} \, dx - 2\int_0^\infty \frac{1}{(e^{2x}+1)x} \, dx$$
Could some help me how to solve it, thanks.
