Improper integral: $\int_0^\infty \frac{\sin^4x}{x^2}dx$
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
29425
$\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
76129
Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
155981
Evaluate an proper integral:$\int_0^\infty x\left(\log\left(\frac1{x^2}\right)\right)^n dx$
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
100485
How do I evaluate the integral $\int_0^{\infty}\frac{x^5\sin(x)}{(1+x^2)^3}dx$?
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
130967
How to show that $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(4x)\cdots\sin(2^kx)\over x^{k+1}}\mathrm dx=2^{0.5(k^2-k-2)}\pi?$
124445
Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
13674
Divergence of an improper integral
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
79633
Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$
103374
A Problem on Improper Integrals
140638
Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.