Integrate $\int_{-\infty}^{\infty} \frac{e^{2020x}-e^{x}}{x\left(e^{2020x}+1\right)\left(e^x+1\right)} \mathop{dx}$ https://ift.tt/eA8V8J

A challenge problem says integrate $$\int_{-\infty}^{\infty} \frac{e^{2020x}-e^{x}}{x\left(e^{2020x}+1\right)\left(e^x+1\right)} \mathop{dx}$$

I thought $u=-x$ helps but I get $I$ so it is even. I also try partial fraction to $$\int_{-\infty}^{\infty} -\frac{1}{x\left(e^{2020x}+1\right)} + \frac{1}{x\left(e^{x}+1\right)} \mathop{dx}$$ Now what? Help please thanks

from Hot Weekly Questions - Mathematics Stack Exchange
Mo Qabar