Evaluate the indefinite integral.

Question

∫(x²-1)/(x²+x-12)dx

Answer 1

integral of (x^2-1)/(x^2+x-12)dx

use polynomial long division

= integral of 1 + (11-x)/(x^2+x-12) dx

linearity

= integral of 1dx + integral of (11-x)/(x^2+x-12)

= x - integral of (x-11)/(x^2+x-12)

rewrite x-11 = (1/2)(2x+1) - (1/2)(23)

linearity

u substitution

u=x^2 +x-12

partial fraction decomposition

= [8ln|x-3| -15ln|x+4|]/7 +x + C