Integrate the function $2x-x^2-x^2$ from $\frac{1}{4}$ to $\frac{3}{4}$

Evaluate the integral

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

Evaluate the integral

$\int_{1}^{3}\cos\left(x\right)^2dx$

Evaluate the integral

$\int_{-5}^{5}\frac{1}{\sqrt{5-x}}dx$

Evaluate the integral

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Evaluate the integral

$\int_{2}^{4}\left(x^2+5x+6\right)dx$

Evaluate the integral

$\int_{2}^{5}\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Evaluate the integral

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$