How to integrate "(x^2) / (x^2 + 8x + 16)"?

Question

I'm having problem solving this exam qns of mine. help will be appreciated. thx.

Answer 1

use the division rule.
int(f(x)/g(x))=
(int(f(x))*g(x)+f(x)*int(g(x))
/(g(x)^2)

Answer 2

int (x^2) / (x^2 + 8x + 16)
= int [ 1 - (8x + 16)/(x^2+8x+16)]
= int [ 1 - 4( 2x + 8 - 4)/(x^2+8x+16)]
= x - 4 int {[(2x+8)/(x^2+8x+16)] - 4/(x+4)^2}
= x - 4 ln (x+4)^2 - 16 (x+4)^(-1) + c
= x - 8 ln Ix+4I - 16 (x+4)^(-1) + c

Answer 3

well first it changes to x^2 / (x+4)^2 then the answer is x= negative 2