# Integration-guess and check

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• November 2nd 2012, 07:40 AM
Greymalkin
Integration-guess and check
Why does $\int \frac{3dx}{2x+5}=\frac{3}{2}ln|2x+5|$?

I get: $\int \frac{3}{2x+5}=ln|2x+5|$
$\frac{d}{dx} ln|2x+5|=\frac{1}{2x+5}$
So by my logic I would just multiply ln|2x+5| by 3, why is the coefficient 3\2 then?
• November 2nd 2012, 07:43 AM
hedi
Re: Integration-guess and check
differentiation should be by the chain rule,so you need to multiply by the derivative of 2x