Question

Integrate $\int \frac{(5x^2+7x+3)}{(x+1)}dx$

Answer 1

$\int \frac{{5x}^2+7x+3}{x+1}dx$

$\int \frac{{5x}^2+5x+2x+2+1}{x+1}dx$

$=\int \frac{{5x}^2+5x}{x+1}dx+\int \frac{2x+2}{x+1}dx+\int \frac{1}{x+1}dx$

$=\int 5xdx+\int 2dx+\int \frac{1}{x+1}dx$

$=\frac{{5x}^2}{2}+2x+ln|x+1|+C$