Solve the differential equation $xy\cdot dx+2\left(x^2+2y^2\right)dy=0$

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

$\int_0^2\left(e^{-x^2}\right)dx$

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{x^2}\right)dx$

Evaluate the integral

$\int_0^1\left(\frac{3}{x^5}\right)dx$

Evaluate the integral

$\int_1^{\infty}\left(\frac{1}{x^2}\right)dx$