Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
10093
$\lim_{x\to \infty}e^{-x^2}\int_x^{x+1/x}e^{t^2}dt$
141516
Solve $\int_0^{+\infty} \Big(\frac{\sin t}{t}\Big)^2 \ dt$
62450
Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
138355
Improper rational/trig integral comes out to $\pi/e$
145335
Is $ \int_0^1{\frac{\sin x}{x}dx} $ convergent?
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
71742
integrate $\int_0^{2\pi} e^{\cos \theta} \cos( \sin \theta) d\theta$
139297
Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
28053
Integral of $\sin(e^t)dt$
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
151063
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
82391
Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$?