Using differentiation under integral sign evaluate $\int_{0}^{\frac {\pi}{2}} \ln (\frac {a+b\sin x}{a-b\sin x}) \cdot \frac {dx}{\sin x} $
63167
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
17925
Vardi's Integral: $\int_{\pi/4}^{\pi/2} \ln (\ln(\tan x))dx $
85949
Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
149913
Evaluate $\iint dy\,dx;\frac{\pi}{4}\leq\theta \leq\frac{3\pi}{4};0\leq r\leq2$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
154065
$\int_{\frac{1}{3}\pi}^{\frac{2}{3}\pi} {\sin(x)\;dx}$ using Riemann sums?
67837
Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
60182
Evaluate $\int\frac{1}{\sin(x-a)\sin(x-b)}\,dx$
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
109416
How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
115598
Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
29602
Integral $ \int_{-\pi/2}^{\pi/2} \frac{1}{2007^x+1}\cdot \frac{\sin^{2008}x}{\sin^{2008}x+\cos^{2008}x}dx $
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
119209
Differentiation wrt parameter $\int_0^\infty \sin^2(x)\cdot(x^2(x^2+1))^{-1}dx$
12604
Evaluate $\int_0^\pi xf(\sin x)dx$