Integral of e^x/(1+e^x) dx
The solution
Detail solution
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There are multiple ways to do this integral.
Method #1
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Let u=ex.
Then let du=exdx and substitute du:
∫u+11du
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Let u=u+1.
Then let du=du and substitute du:
∫u1du
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The integral of u1 is log(u).
Now substitute u back in:
log(u+1)
Now substitute u back in:
log(ex+1)
Method #2
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Let u=ex+1.
Then let du=exdx and substitute du:
∫u1du
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The integral of u1 is log(u).
Now substitute u back in:
log(ex+1)
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Now simplify:
log(ex+1)
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Add the constant of integration:
log(ex+1)+constant
The answer is:
log(ex+1)+constant
The answer (Indefinite)
[src]
/
|
| x
| E / x\
| ------ dx = C + log\1 + E /
| x
| 1 + E
|
/
∫ex+1exdx=C+log(ex+1)
The graph
−log(2)+log(1+e)
=
−log(2)+log(1+e)
Use the examples entering the upper and lower limits of integration.