Question

How do you integrate `int x / ((x-5)(x+3))dx` using partial fractions?

Answer 1

I found: `1/8[5ln|x-5|+3ln|x+3|]+c`

Explanation:

The argument can be written as:
`x/((x-5)(x+3))=1/8[5/(x-5)+3/(x+3)]`
The integral becomes:
`1/8int[5/(x-5)+3/(x+3)]dx=`
That can be written as:
`=1/8[int5/(x-5)dx+int3/(x+3)dx=1/8[5ln|x-5|+3ln|x+3|]+c`