Showing that $ \int_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)}dx$ diverge
63756
Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$
51284
$\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
63380
Show that the series $\sum_{n=2}^{\infty} \frac{1}{n\, (\log n)^s}$ converges for $s >1$ and diverges for $s=1$
75423
Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
119147
How to prove that $\sum_{n=1}^{\infty}\frac{|\sin{(n\theta_0)}|}{n}$ diverges for given $\theta_0\in (0,\pi)$?
124463
Integral from $0$ to $\infty$ of $\ln(x)/e^x$
106812
Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
149658
How would you show that the series $\sum_{n=1}^\infty \frac{(2n)!}{4^n (n!)^2}$ diverges?
31199
Divergence $\int_{-\pi}^{\pi} |D_n(x)|dx$ for Dirichlet kernel as $n\to\infty$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
1392
$\int_{0}^{\infty}{\left(x^3\cdot(e^x-1)^{-1} \right)}dx$
111775
$\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
153905
If $\sum_{n_0}^{\infty} a_n$ diverges prove that $\sum_{n_0}^{\infty} \frac{a_n}{a_1+a_2+...+a_n} = +\infty $
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$