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Natural log differentiation and back

psi20
in Analysis and Calculus

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Hey. I can't understand why this is weird.

 

I'm not familiar with the math notation so I'll explain it in words, it's not hard to explain.

 

Take the derivative of ln(5 x^4). You get 4/x

If you take the integral of 4/x, you get 4 ln |x| + C or ln (x^4) + C. But this is different than what the original function was, and that's what's confusing me.

ln(5 x^4) = ln(5) + ln(x^4)

Therefore if C=ln(5) you have your old func back.

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