Question

Find the antiderivative of (x - 5)/(x^2 - 1)

Answer 1

partial fractions again :)

Answer 2

\[\int\limits \frac{ x-5 }{ (x^2-1) }\]

Answer 3

:l

Answer 4

Can't you use \[\int\limits \frac{ 1 }{ x^2-a^2 }=\frac{ 1 }{ 2a }\ln |\frac{ x-a }{ x+a }|+C?\]

Answer 5

yes it is correct, but they likely won't have a formula sheet on the exam. They must be able to reach that without memorizing the formula I believe.

This would be by solving for A and B in the case of:

\[\int\limits_{}^{} \frac{ x-5 }{ (x-1)(x+1) } dx = \int\limits_{}^{} \frac{ A}{ (x-1)} + \frac{ B }{ x+1 } \]

Answer 6

okay

Answer 7

so i cross multiply next?

Answer 8

yes you want to make the denominator the same and to solve for A and B using the values on the left

Answer 9

okay