Integral $ I=\int_{-r}^r \int_{-\sqrt{r^2-x^2}}^{\sqrt{r^2-x^2}} \sqrt{1 - \frac{x^2 + y^2}{x^2 + y^2 - r^2}} dy dx $
129318
Integrate via substitution and derivation rule
132388
Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
45872
Integration: $\int\frac{1}{(x^2+x+1)^{1/2}} dx$
143585
Solve the integral $\frac 1 {\sqrt {2 \pi t}}\int_{-\infty}^{\infty} x^2 e^{-\frac {x^2} {2t}}dx$
156215
Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$
42992
How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$
81914
Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$
94395
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
6852
Integral of $\int \frac{x \sin{x} \cos{x}}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} dx $
152977
Integrate $\int\sqrt{x+\sqrt{x^{2}+2}} dx$ .
6830
Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
81533
Integrating $\int_1^2 \int_0^ \sqrt{2x-x^2} \frac{1}{((x^2+y^2)^2} dydx $ in polar coordinates
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
145590
Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$