Evaluate $\int_0^{\infty} x^2\,e^{-x^2}\,dx$ if it is convergent.
29680
How to determine $\int x^2 e^{-x^2}\mathrm dx$?
56867
Convergence proof that involves integral
89028
Evaluate the integral $\int e^{-x}x^n dx$
57224
Compute $\int_0^\infty \frac{dx}{1+x^3}$
32423
Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$
9518
Evaluate: $ \int_0^1 \int_y^1 e^{x^2 }dxdy$
133160
Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
121736
An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$
61515
Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration
33005
How to evaluate $\int_{0}^{+\infty}\exp(-ax^2-\frac b{x^2})\,dx$ for $a,b>0$
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
157725
does $\int _{1}^{\infty}\frac{p(x)}{e^x}$ converge?
81621
How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
42758
How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$