Prove the trigonometric identity $\cot\left(x\right)+\tan\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Find the integral

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

Find the integral

$\int\frac{x^3}{x^3+1}dx$

Find the integral

$\int\frac{\sqrt{25-x^{2}}}{x}dx$

Find the integral

$\int\frac{2x^5-10x^3-2x^2+10}{x^2-5}dx$

Find the integral

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

Find the integral

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

Find the integral

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