Question

Evaluate: $\int \frac{(x^2+2)dx}{x+1}$

Answer 1

$\int \frac{(x^2+2)dx}{x+1}=\int \frac{x^2-1+3}{x+1}dx$

$=\int [\frac{(x-1)(x+1)}{(x+1)}+\frac{3}{x+1}]dx$

$=\int (x-1)dx+\int \frac{3}{x+1}dx$


$=\frac{x^2}{2}-x+3\log \mid x+1\mid +c$

where $c$ is constant of integration
Hence, the required integration is $=\frac{x^2}{2}-x+3\log \mid x+1\mid +c$ .