INTEGRATION. Why both results are the same?

Question

$4 ln(x^2-4) + x^2 - 4 + c$
and
$4 ln(x^2-4) + x^2 + c$

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Answer 1 · 2018-06-07T16:58:17

See explanation

Remember $color(red)(-4$ is just a constant, so

$4ln(abs(x^2-4))+x^2-4+C$

$=4ln(abs(x^2-4))+x^2+C_1$

Where, $color(blue)(C_1=-4+C$