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

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

$\int_1^{25}\frac{\left(\left(lnx\right)^5\right)}{4x}dx$

Evaluate the integral

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

Evaluate the integral

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