Integrate $\int_0^\infty\frac{\cos(\alpha x) - \cos(\beta x)}{x}dx$
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
9730
Solve the integral $\int_0^\infty x/(x^3+1) dx$
80903
Help with integrating $\int_0^{\infty} \frac{(\log x)^2}{x^2 + 1} \operatorname d\!x$ - contour integration?
128600
How to evaluate this integral$\int_{-\infty}^\infty\dfrac{\omega^\alpha e^{i\omega t}}{(\omega_0^2-\omega^2)^{2}+4(\zeta\omega_0\omega)^2}\,d\omega$
132000
Calculate $\int_0^\infty\frac{\sin x}xdx$ by integration of a suitable function along given paths
16800
Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
75267
integrate the following function: $\int_{0}^{\infty} \frac{\log{x}}{x^{2}+a^{2}} \ dx$
108554
Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
2411
Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$
29383
Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus
37097
Integral $\int \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx$
111636
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
60654
Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
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$
14385
Solve $\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$ without complex integration.
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
81621
How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?