Question

Int(x-1)(x-2)/x+4 dx ?

Answer 1

`I=1/2x^2-7x+30ln(abs(x+4))+C`

Explanation:

I assume you meant

`I=int((x-1)(x-2))/(x+4)dx`

`color(white)(I)=int(x^2-3x+2)/(x+4)dx`

By long division

`I=intx-7+30 1/(x+4)dx`

`color(white)(I)=intxdx-int7dx+30int1/(x+4)dx`

`color(white)(I)=1/2x^2-7x+30ln(abs(x+4))+C`