# u-substitution yields a different answer

When I compute the indefinite integral of ln(x + x^2), I get 2 answers from 2 different methods.

First method: integration by parts => u-substitution Answer = xln(x + x^2) - 2 (x + 1) + ln l x + 1 l + C

Second method: integration by parts => long division Answer = xln(x + x^2) - 2x + ln l x + 1 l + C

I think both are correct, since they only differ by a constant term. Do I get the same mark in exam if I give either of those?

• Here's how to use MathJax :) May 4 '19 at 7:19

$$-2(x+1) \ + \ c$$ can be written as $$-2x -2+c = -2x +c'$$ where $$c'$$ is another constant and in the indefinite integral constants may vary as it represents a family of curves.