Question

∫(3x^2-2)/X^2-2x-8) ∫(3x^2-2)/X^2-2x-8) @Mathematics

Answer 1

write
\[\frac{3x^2 - 2}{x^2 - 2x - 8} = 3 +\frac{23}{3} \frac{1}{x-4} - \frac{5}{3} \frac{1}{x+2}\]

now the integration is easy, the answer is
\[3x + \frac{23}{3} \ln (x-4) -\frac{5}{3} \ln (x+2) + const.\]