How do I prove this integral?
52978
Interesting integral related to the Omega Constant/Lambert W Function
103164
Calculate Integral using residue theorem
104125
How prove this inequality??
32657
What is the value of this Integration?
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
20021
Convolution integral $\int_0^t \cos(t-s)\sin(s)\ ds$
20415
Show that the integral of a positive function is positive
110368
Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$
129578
A result of Stieltjes Integral
8358
Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
83531
Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
154067
Not sure how to go about solving this integral
66304
How to evaluate these integrals by hand
79686
How can I prove these statements?
136981
How can I solve this integral using the Residue theorem?