Prove the following equality: $\int_{0}^{\pi} e^{4\cos(t)}\cos(4\sin(t))\;\mathrm{d}t = \pi$
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
60654
Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
21088
Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
54175
Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$
150756
Equality of integrals
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
71742
integrate $\int_0^{2\pi} e^{\cos \theta} \cos( \sin \theta) d\theta$
129042
Prove that $\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
157364
$\int_{-2}^{2} \sin(x^5)e^{(x^8\sin(x^4))} dx$
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
12653
Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$
97253
How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
109099
Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
26608
How to show that $\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3?$