New posts in Definite Integrals

Evaluating two integrals involving $\tan^{-1}\left(\frac{\sqrt{x(1-x)}}{x+\frac12}\right)$

Alternative ways to evaluate $\int_0^1 x^{2n-1}\ln(1+x)dx =\frac{H_{2n}-H_n}{2n}$

How to evaluate $ \int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{\sqrt{1+x^2}} \, \mathrm{d}x $

Challenging integral: $\int_0^{\pi/2}x^2\frac{\ln(\sin x)}{\sin x}dx$

Evaluate $3\int_{0}^{2\pi} \sin(t) \cos(t) \,{\rm d}t$

Proving $\int_{0}^{1} \frac{\tanh^{-1}\sqrt{x(1-x)}}{\sqrt{x(1-x)}}dx=\frac{1}{3}(8C-\pi\ln(2+\sqrt{3}))$ for an identity of Srinivasa Ramanujan

How to evaluate $\int _0^1\frac{\ln ^2\left(1-x\right)\ln ^5\left(1+x\right)}{1+x}\:dx$

How can I prove $\int_{0}^{1} \frac {x-1}{\log(x) (1+x^3)}dx=\frac {\log3}{2}$

Is there an efficient way of showing $\int_{-1}^{1} \ln\left(\frac{2(1+\sqrt{1-x^2})}{1+x^2}\right)dx = 2$?

Computing $\int_0^1 \frac{\arcsin \sqrt x}{x^2-x+1} dx$