Evaluating $\int_{0}^{\pi}\ln (1+\cos x)\, dx$
125523
How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?
109416
How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
121071
Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
90245
Computing $\int^1_0 \frac{p^2-1}{\text{ln } p}dp$
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
156485
How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$?
74822
How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
135519
How to approach solving $\int_0^{\pi/2} \ln(a^2 \cos^2 x +b^2 \sin^2 x ) dx$
106812
Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
151563
Evaluate: $\int_{0}^{\pi}\frac{\cos 2017x}{5-4\cos x}dx$
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
153867
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
96414
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
36586
Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$