x^2+4x-3/x-1 dx=?

Question

substitution and intergration. please show or explain answer.

Answer 1

Let's divide x^2 + 4x -3 by x-1

x^2 + 4x - 3 = x^2 -x + 5x - 5 + 2 = (x-1)(x + 5) + 2

(x^2+4x-3)/(x - 1) = (x + 5) + 2/(x - 1)

int (x^2+4x-3)/(x - 1) dx = int (x + 5) + 2/(x - 1) dx =

= (x^2)/2 + 5x + 2 ln|x - 1| + C