Integral of $\int_{\mathbb{R}}e^{-\frac{x^{2}}{2}}\left(\cos\left(\pi nx\right)\right)dx$
104138
How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
34907
Show that $\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
94395
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
31660
Integral $\int_{0}^{1}\left\{\frac{1}{x}\right\}\left\{\frac{1}{1-x}\right\}\left\{1-\frac{1}{x}\right\} d x=?$
121310
Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$
148826
Integral of $ 1 \, / \, (1 + a \, \cos(x) )$
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
24558
Show that $\frac{1}{\sqrt{2\pi}} \cdot \left(\int_{- \infty}^{\infty} e^{itx} \cdot e^{-\frac{1}{2}t^2 } dx \right) = e^{-\frac{1}{2}t^2}$
90313
Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
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$
55738
Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
137060
Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
85081
$\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
10036
Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$
60944
Evaluating an integral with ${\mathrm{d}t}$ in the numerator, $\int \frac{\mathrm{d}t}{\cos(t)^2}$.
8606
Calculate $\int^{n+1}_1 \frac{(\{x\})^{[x]}}{[x]}dx$ where $n\in\mathbb{N}$, $[x]$ is the integer part of $x$ and $\left\{ x\right\} =x-[x]$.