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What is the Integration of dx/(x+e^x)


Kshama Chakraborty 14th Sep, 2019
Answer (1)
rajaman9300 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.

1 Comment
Comments (1)
15th Dec, 2020
this is nit the question that he wants
Reply

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