Stuck on this integration $\int_0 ^\infty \frac{1}{1+x^2} \cos(kx) dx =\frac{\pi}{2}e^{-k}$
13978
Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis
90313
Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
7835
Tricky elementary integral $\int_{0}^{\frac{\pi}{2}}x\cot(x)dx$.
71700
How to solve $\int_0^\pi{\frac{\cos{nx}}{5 + 4\cos{x}}}dx$?
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
85081
$\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
63016
Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
108554
Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
53519
Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
80903
Help with integrating $\int_0^{\infty} \frac{(\log x)^2}{x^2 + 1} \operatorname d\!x$ - contour integration?
64417
Integration of $\int \frac{x^2+20}{(x \sin x+5 \cos x)^2}dx$
44737
$ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
104138
How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
18672
Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
110922
What are different ways to compute $\int_{0}^{+\infty}\frac{\cos x}{a^2+x^2}dx$?
119410
Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$