Integral using gamma function $\int_0^1 x^a(1-x)^b dx = \frac{\Gamma(1 + a) \Gamma(1 + b)}{\Gamma(2 + a + b)} $
48651
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
31660
Integral $\int_{0}^{1}\left\{\frac{1}{x}\right\}\left\{\frac{1}{1-x}\right\}\left\{1-\frac{1}{x}\right\} d x=?$
60654
Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
17996
Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
145590
Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
67322
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
140122
Integral: $\int_0^1\frac{\mathrm{Li}_2(x^2)}{\sqrt{1-x^2}}dx$
73489
How is the Integral of $\int_a^bf(x)~dx=\int_a^bf(a+b-x)~dx$
62840
Seemingly Simple Integral $\int_0^1\frac{x^2\ln x}{\sqrt{1-x^2}}dx$.
47793
Integral $\int_0^1\sqrt{1-x^4}dx$
2411
Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$
109416
How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
63167
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
138174
Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
104094
Integral of $\frac{1}{(1+x^2)^2}$