Compute $\int\limits_0^{\pi}\ln\left(1-\cos\left(t\right)\right)\ dt$
7388
Evaluate: $\int_0^{\pi} \ln \left( \sin \theta \right) d\theta$
79466
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
27790
Evaluating $\int_0^{\large\frac{\pi}{4}} \log\left( \cos x\right) \, \mathrm{d}x $
63237
Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
122361
Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
93174
Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$
151127
Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
130935
Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
64800
Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
135519
How to approach solving $\int_0^{\pi/2} \ln(a^2 \cos^2 x +b^2 \sin^2 x ) dx$
16712
Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$
8358
Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $
31448
Calculate $\int\left( \sqrt{\tan x}+\sqrt{\cot x}\right)dx$
6571
A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
124209
How is $\ln(-1) = i\pi$?
4224
Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$