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

Evaluate the integral

$\int_2^{\infty}\left(\frac{1}{x^2+x-2}\right)dx$

Evaluate the integral

$\int_{-1}^2\frac{3x}{x+4}dx$

Evaluate the integral

$\int_9^4\left(\frac{x^2}{x+1}\right)dx$

Evaluate the integral

$\int_e^{\infty}\left(\frac{1}{x\left(\ln\left(x\right)\right)^3}\right)dx$

Evaluate the integral

$\int_2^{\infty}\left(\frac{lnx}{x}\right)dx$

Evaluate the integral

$\int_0^1\left(\ln\left(1+x\right)\right)dx$

Evaluate the integral

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