Question

How do you integrate `int(x)/((x+4)(x+6)(x+1))` using partial fractions?

Answer 1

`2/3 ln (x+4) -3/5 ln (x+6) -1/15 ln (x+1)+C`

C=the constant of inegration

Explanation:

`x=A(x^2+7x+6)+B(x^2+5x+4)+C(x^2+10x+24)`

`A=2/3`
`B=-3/5`
`C=-1/15`
`int x/((x+4)(x+6)(x+1)) dx = int A/(x+4) dx+ int B/(x+6) dx+int C/(x+1) dx`