$\frac{\int_0^1x^n\sqrt{1-x^2}}{\int_0^1x^{n-2}\sqrt{1-x^2}}$
68639
given $I_{n}=\int^1_{0}x^n\sqrt{1-x^2}dx$, then finding value of $ \frac{I_{n}}{I_{n-2}}$
157931
Contour integration of $\int \frac{dx} {(1+x^2)^{n+1}}$
8642
Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
87065
Recurrence relation for the integral, $ I_n=\int\frac{dx}{(1+x^2)^n} $
69803
An elementary proof of $\int_{0}^{1}\frac{\arctan x}{\sqrt{x(1-x^2)}}\,dx = \frac{1}{32}\sqrt{2\pi}\,\Gamma\left(\tfrac{1}{4}\right)^2$
19631
Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
38511
Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
91333
How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
125069
Help with $\int \frac 1{\sqrt{a^2 - x^2}} \mathrm dx$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
104691
Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
39629
Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
119410
Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
100817
Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.