Demonstration of $\int_{-a}^a \frac{f(x)}{1+e^x} \,dx= \int_0^a f(x) \,dx$
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
79575
The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{0}^{f(a)}f^{-1}=af(a)$
4971
$\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
27195
Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
142834
An integral : $\int_{-a}^a \frac{\cos(\pi n x/a)}{x^2+a^2}\mathrm dx$
34762
Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?
21390
How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
113066
Calculate $\int_0^1f(x)dx$
102649
Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
63956
Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
89499
Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.