How do you evaluate the integral $int 2^x/(2^x+1)$ ?

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Answer 1 · 2018-03-23T02:40:42

$ln(2^x+1)/ln 2+C$

Since $d/dx(2^x+1)=2^x ln 2$ , we have

$int 2^x/(2^x+1)dx = 1/ln 2 int {d(2^x+1)}/(2^x+1) = ln(2^x+1)/ln 2+C$

How do you evaluate the integral int 2^x/(2^x+1)int 2^x/(2^x+1)?