Improper integral of $\frac{\sin (\pi a t) \sin (\pi b t)}{t^2}$ depends only on the smaller of $a,b$
62173
How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
15324
A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$
18672
Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
6892
Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?
32270
Integral depending on a parameter
127343
Trigonometric integral involving the fractional part function
116498
Convergence of improper integral $\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
138355
Improper rational/trig integral comes out to $\pi/e$
60654
Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
10341
complex integration $\frac{1-|a|^{2}}{\pi}\int_{L}\frac{|dz|}{{|z+a|}^{2}}$
151127
Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
13674
Divergence of an improper integral
1416
closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$