Question

How do I integrate (x^2-6)/(x^2-9)?

Answer 1

Hm, if substitution doesn't work then try integration by parts.
(x^2 - 6)(x^2-9)^-1

Answer 2

what if there is a partial fraction decomposition of this quotient?

Answer 3

divide, then use partial fractions

Answer 4

actually there is an easy gimmick for division
write the numerator as
\[x^2-9+3\]

Answer 5

then you get
\[\int 1dx-3\int\frac{dx}{x^2-9}\]

Answer 6

@satellite73 nice insight

Answer 7

oops that was wrong
\[\int 1dx+3\int\frac{dx}{x^2-9}\]

Answer 8

@blurbendy thanks
second part use partial fractions

Answer 9

ok thanks for your help. I guess I thought there was a more conventional approach.