Prove the trigonometric identity $\frac{1+\tan\left(y\right)}{1+\cot\left(y\right)}=\tan\left(y\right)$

Find the integral

$\int\frac{1}{e^{2x}-3e^x}dx$

Find the integral

$\int\frac{1}{1+e^{-2x}}dx$

Find the integral

$\int x^2e^{2x+1}dx$

Find the integral

$\int x^2e^xdx$

Find the integral

$\int\left(\frac{\cos\left(x\right)}{x}\right)dx$

Find the integral

$\int\frac{cos\left(x\right)}{x}dx$

Find the integral

$\int16xe^{4x}dx$