About the integral $\int_{0}^{1}\frac{\arctan(x)\,dx}{\sqrt{x(1-x^2)}}$ and related hypergeometric functions
69803
An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$
88815
Integral of $\int \frac{dx}{\sqrt{x^2 -9}}$
147759
Integral $ \dfrac { \int_0^{\pi/2} (\sin x)^{\sqrt 2 + 1} dx} { \int_0^{\pi/2} (\sin x)^{\sqrt 2 - 1} dx} $
31063
Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
65562
Proving the inequality $\arctan\frac{\pi}{2}\ge1$
36128
Using differentiation for computing $\int_{0}^{1}\frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx$
24182
Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
127343
Trigonometric integral involving the fractional part function
135447
Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
51216
Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$
29970
Bounds of $I=\int_0^1\frac{\sin x}{\sqrt x}$ and $J=\int_0^1\frac{\cos x}{\sqrt x}$?
42279
Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $
126236
General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
23018
Integral $\int_a^\infty \frac{\arctan(x+b)}{x^2+c}dx$
47793
Integral $\int_0^1\sqrt{1-x^4}dx$