Question

How do you integrate `int (3x + 2) / [(x - 1)(x + 4)]` using partial fractions?

Answer 1

We have that

`(3x+2)/[(x-1)(x+4)]=2/(x+4)+1/(x-1)`

Hence

#int (3x+2)/[(x-1)(x+4)]dx=int 2/(x+4)dx+int 1/(x-1)dx= 2*logabs(x+4)+logabs(x-1)+c#