Question

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

Answer 1

$\int \frac{x^{3}dx}{x+2}$ put x+2=t x

x=t-2

dx=dt

=$\int \frac{(t-2{)}^3}{t}dt$

=$\int \left(\frac{t^3-6t^2+12t-8}{t}\right)dt$

=$\int (t^2-6t+12-\frac{8}{t})dt$

$=\frac{t^3}{3}-3t^2+12t-8ln\left(t\right)+c$

$=\frac{(x+2{)}^3}{3}-3(x+2{)}^2+12(x+2)-8ln(x+2)+c$