Integral of $\frac{e^x}{5+2e^x}$ Regarding the integral of this term$\frac{e^x}{5+2e^x}=\frac{e^x}{2(\frac{5}{2}+e^x)}$
Is the answer $\frac{1}{2} \ln(\frac{5}{2} +e^x)$ or $\frac{1}{2} \ln(5+2e^x)$?
When I substitute $u= \frac{5}{2}+e^x$ I get the first one, when it's $u=5+2e^x$, then it is the second one...

$$C + \frac 12 \ln(5+2e^x ) =C + \frac 12\ln[2(\frac 52 +e^x)]=C +\frac12\ln 2 + \frac 12 \ln\left(\frac 52 + e^x\right)  $$ the two antiderivatives differ by a constant.
