Integrate the function $\frac{1}{1+2\sin\left(x\right)^2}$ from 0 to $\pi $

Evaluate the integral

$\int_2^3\frac{1}{\sqrt{x-1}}dx$

Evaluate the integral

$\int_0^1\left(\frac{ln\left(x\right)}{x}\right)dx$

Evaluate the integral

$\int_0^1\left(\frac{x}{\left(4-x^2\right)^{\frac{3}{2}}}\right)dx$

Evaluate the integral

$\int_1^2x\ln\left(x\right)dx$

Evaluate the integral

$\int_0^3\sqrt{9-x^2}dx$

Find the integral

$\int\left(\frac{arctan\left(2x\right)}{x}\right)dx$

Evaluate the integral

$\int_1^{\infty}\left(\frac{ln\left(x\right)}{x}\right)dx$