Integrate the function $\frac{x^2\cos\left(\frac{x}{5}\right)}{\left(x^2+25\right)^2}$ from 0 to $\infty $

Evaluate the integral

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

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

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

Evaluate the integral

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

Evaluate the integral

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