Answer
$\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}ln|2^{x}+1|+C$
Work Step by Step
Evaluate the integral $\int \frac{2^{x}}{2^{x}+1}dx$
Consider $2^{x}=t$ and $dx=\frac{dt}{2^{x}ln2}$
Now, $\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}\int\frac{dt}{t+1}$
$=\frac{1}{ln2}ln|t+1|+C$
Hence, $\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}ln|2^{x}+1|+C$