Question

integrate 1/(x^2-x-6)

Answer 1

i believe they need you to decompose the fraction, if possible

Answer 2

(x^2-x-6)=(x-3)(x+2)
1/(x-3)(x+2)=A/x-3+B/(x+2)
A(x+2)+B(x-3)/(x^2-x-6)

A(x+2)+B(x-3)=1
when x=3
A(5)=1
A=1/5
when x=-2
B(-5)=1
B=-1/5
\[1/5\int\limits_{}^{}1/(x+2)dx-1/5\int\limits_{}^{}1/(x-3)dx\]
1/5(ln(x+2))-1/5ln(x-3)+C