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This question is seriously weird: Maths A level calculus question.

How come 0.5ln(x) differentiates to 1/2x, but 1/2x integrates to 0.5ln(2x)? My friend just asked me this and now my brain is hurting. Any help?

SOLVED: Thanks to reddit and HippityLongEars for those that are interested here is the answer.
Both answers are correct.
Indefinite integrals are only correct up to a constant, which is why your answers to indefinite integrals usually require a "+C" at the end.
Using a property of logarithms:
0.5 ln(2x) = 0.5 [ln(2) + ln(x)] = 0.5 ln(2) + 0.5 ln(x)
So the two functions are the same, only off by a constant.
(edited 6 years ago)

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