Integrate the function $\frac{x}{x^2+4}$ from $-1$ to $2$

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_3^{\infty}4e^{\left(2x-4\right)}dx$

Evaluate the integral

$\int_3^{\infty}\left(4e^{\left(2x-4\right)}\right)dx$

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

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