Question

Find the antiderivative of (x - 5)/(x^2 - x - 2)

Answer 1

\[\frac{x - 5? }{ x^2 - x - 2}\]

Answer 2

have to take partial factorial it first. then take integral

Answer 3

\[ = \frac{A}{x-2}+\frac{B}{x+1}\]
A(x+1)+ B(x-2) = x-5
if x = -1 the equation above turns to -3B = -6 --> B =2
if x = 2, the equation above turns to 3A = -3 --> A = -1
so, yours can be written like \[-\frac{1}{x-2} + \frac{2}{x+1}\]
then, take integral that sum, you get 2ln(x+1) -ln (x-2)