How to calculate this improper integral $\int_{0}^{+\infty}\frac{x}{\mathrm{e}^x-1}\mathrm{d}x$?
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
102399
Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $
8642
Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
67263
Compute integral $\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$
94395
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
34855
Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$
40881
Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
43329
Why is $\int_{-1}^{1} \frac{1}x \mathrm{d}x$ divergent?
156215
Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$
41738
Best way to integrate $ \int_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $
101546
Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
138355
Improper rational/trig integral comes out to $\pi/e$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
87273
Evaluate the integral $\int_0^{\infty} \lfloor x \rfloor e^{-x}\mathrm dx$
95426
How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$