Question

How do you use partial fraction decomposition to decompose the fraction to integrate `(2x-82)/(x^2+2x-48)`?

Answer 1

`d/dx(x^2+2x-48)=2x+2`

`(2x-82)/(x^2+2x-48) = (2x+2-84)/(x^2+2x-48)`

`(2x-82)/(x^2+2x-48) = (2x+2)/(x^2+2x-48)-(84)/(x^2+2x-48`

By above partial fraction the function can easily be integrated.