How can changing the order of integration be used to solve the integral $\int_0^\infty \frac{\cos{(\alpha x)}-\cos{(\beta x)}}{x}\, dx$
38773
Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $
80428
Convergence of $\int\limits_1^{\infty}x^\alpha\sin(x^\beta)dx$
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
15324
A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$
133485
How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
14385
Solve $\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$ without complex integration.
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
69124
Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
90339
Integral involving Cosine function
67322
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
62109
$\int_{-\infty}^{\infty} \frac{\cos(αx)}{(x^2+1)(x^2+4)} \mathrm dx$ using Complex methods
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
51489
Simplifying the integral $\int\frac{dx}{(3 + 2\sin x - \cos x)}$ by an easy approach
91196
Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$