find the integral of...?

Question

find the integral of (3x^2 -3x+4)/(-x^2 +2x+15)

Answer 1

It's nasty (integrals have a way of being nasty ☺), but break it up into the sum of 3 integrals. I got
-3x -8ln(x-5)+5ln(x+3) +C

Doug

Answer 2

(3x^2 - 3x + 4)/(-x^2 + 2x + 15)

-(3x^2 - 3x + 4)/(x^2 - 2x -15)

-(3x^2 - 3x + 4)/(x+3)(x-5)

splitting into partial fractions

-[(3x + 4)/(x+3) + 8/(x-5)]

-[3(x+3)(x+3) - 4/(x+3) + 8/(x-5)]

-3 ∫dx + 4∫dx/(x+3) dx - 8∫dx(x-5)

-3 x + 4ln(x+3) - 8ln(x-5) +c