Question Number 83104 by 09658867628 last updated on 28/Feb/20
$$\int\frac{{e}^{{x}} {dx}}{\mathrm{3}+{e}^{{x}} } \\ $$
Answered by MJS last updated on 28/Feb/20
![∫(e^x /(3+e^x ))dx= [t=e^x → dx=(dt/e^x )] =∫(dt/(t+3))=ln (t+3) =ln (3+e^x ) +C](https://www.tinkutara.com/question/Q83106.png)
$$\int\frac{\mathrm{e}^{{x}} }{\mathrm{3}+\mathrm{e}^{{x}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{e}^{{x}} \:\rightarrow\:{dx}=\frac{{dt}}{\mathrm{e}^{{x}} }\right] \\ $$$$=\int\frac{{dt}}{{t}+\mathrm{3}}=\mathrm{ln}\:\left({t}+\mathrm{3}\right)\:=\mathrm{ln}\:\left(\mathrm{3}+\mathrm{e}^{{x}} \right)\:+{C} \\ $$