Question

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

Answer 1

We have,

$I=\int \frac{x^3+x^2+1}{x+1}dx$

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

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

$I=\frac{x^3}{3}+\ln (x+1)+C$

Hence, this is the answer.