Question

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

Answer 1

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

$=\int \left[\frac{(x-2)(x^2+2x+4)+8}{(x-2)}\right]dx$

$=\int \left[\right(x^2+2x+4)+\frac{8}{x-2}]dx$

$=\frac{x^3}{3}+x^2+4x+8ln(x-2)+c$

$\therefore \int \frac{x^3}{x-2}dx=\frac{x^3}{3}+x^2+4x+8ln(x-2)+c$

$x^2+2x+4$

$x-2)x^3$

$x^3-2x^3$

________________

$2x^2$

$2x^2-4x$

_____________

$4x$

$4x-8$

__________

$8$.