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?

  • $\begingroup$ Here's how to use MathJax :) $\endgroup$ – Toby Mak May 4 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.

And, yes both are equivalent.


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