Question

Find the partial fractions decomposition and an antiderivative.

Answer 1

@Twis7ed

Answer 2

Have you tried it yourself?

Answer 3

(x-5)/(x^2 -1)
(x^2 - 1) == (x-1)(x+1)


A/(x-1) + B/(x+1)

Ax + A + Bx - B

A + B = 1 (Which is the coefficient of x)
A - B = -5 (Which is the coefficient of x^0)

A = 1-B

(1-B) - B = -5
1 - 2B = -5
-2B = -6
2B = 6
B = 3

A = -2

-2/(x-1) + 3/(x+1) = (x-5)/(x^2 - 1)

Answer 4

ohh ok now i see my mistake thanks!