What is the Integration of dx/(x+e^x)
Answer (1)
Student Expert
14th Sep, 2019
Hello Kshama
dx/(1+e^x) = e^xdx/e^x(1+e^x)
let, 1+e^x = z
e^xdx = dz
e^xdx/e^x(1+e^x)= dz/z(z-1)
={ z-(z-1)}dz/z(z-1)
=dz/(z-1)-dz/z
Integrating we get,
ln|z-1|- ln|z| +c [ c is integration constant]
= ln|e^x| - ln|1+e^x| +c
=ln|e^x/(1+e^x)| + c
Mention, if i am wrong.
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