Integrating $\int_{0}^{\infty} \frac{(\log x)^2}{x^2+x+1}$ using residue theorem
83876
Definite integral, quotient of logarithm and polynomial: $I(\lambda)=\int_0^{\infty}\frac{\ln ^2x}{x^2+\lambda x+\lambda ^2}\text{d}x$
108357
Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
155919
Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
80903
Help with integrating $\int_0^{\infty} \frac{(\log x)^2}{x^2 + 1} \operatorname d\!x$ - contour integration?
65982
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
29546
Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.
119410
Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
115089
Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
129947
Integral of $\log(\sin(x))$ using contour integrals
79466
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
6571
A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
86857
Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$
21464
Finding the integral $\int_0^1 \frac{x^a - 1}{\log x} dx$