Show that $\int_{0}^{\infty}\frac{x^2}{1+x^5}dx = \frac{\pi}{5\sin(\frac{2\pi}{5})}$
5537
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
63237
Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
6852
Integral of $\int \frac{x \sin{x} \cos{x}}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} dx $
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
1416
closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
89956
Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$?
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
29425
$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
35319
I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$
79633
Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
31792
show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
64417
Integration of $\int \frac{x^2+20}{(x \sin x+5 \cos x)^2}dx$