differentiation under the integral sign $\int_{0}^{\pi}\ln\left(1-2r\cos x +r^2 \right)dx$
6483
Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
136385
Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$
17435
Big integral sign
142516
Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
130935
Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
155919
Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$
34905
Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$
27790
Evaluating $\int_0^{\large\frac{\pi}{4}} \log\left( \cos x\right) \, \mathrm{d}x $
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
24974
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
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) $
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
96112
Differentiating $ \left( 1 - \frac {1}{x} \right)^x $