Question

Integrate the following with respect to x.

`x^3/(x + 2)`

Answer 1

= `int x^3/((x + 2))  "d"x`

= `int (x^3 + 8 - 8)/((x + 2)) "d"x`

= `int ((x^3 + 2^3)/((x + 2)) - 8/((x + 2))) "d"x`

= `int [((x + 2)(x^2 - 2x + 4))/((x + 2)) - 8/((x + 2))]  "d"x`

= `(xx^3/3 - (2x^2)/2 + x) - 8 log |x + 2| + "c"`

= `x^3/3 - x^2 + 4x - 8 log |x + 2| + "c"`