About the integral of $\frac{\sin(ax)}{e^{2\pi x}-1}$ over the positive real line
86712
Use rectangular contour to integrate $\int_{0}^{\infty}\frac{\sin(ax)}{e^{2\pi x}-1}dx$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
48408
Definite Integral of $\sin(\sin x)$
48651
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
138355
Improper rational/trig integral comes out to $\pi/e$
83325
Integral of $\frac{\sqrt{x^2+1}}{x}$
18836
Complex integral over a circle
58616
A generalization for Serret's integral $\int_0^a \frac{\ln(1+ax)}{1+x^2}dx$
11129
Show that $\int_0^ \infty \frac{1}{1+x^n} dx= \frac{ \pi /n}{\sin(\pi /n)}$ , where $n$ is a positive integer.
152339
Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
31792
show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
148746
Calculating $\int\frac{e^{iz}}{z}\, dz$ on the semi-circle given by $re^{i\theta}$ where $\theta:\,0\to\pi$
126046
solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $