Integral of e^x/(e^x+2) dx
The solution
Detail solution
-
There are multiple ways to do this integral.
Method #1
-
Let u=ex.
Then let du=exdx and substitute du:
∫u+21du
-
Let u=u+2.
Then let du=du and substitute du:
∫u1du
-
The integral of u1 is log(u).
Now substitute u back in:
log(u+2)
Now substitute u back in:
log(ex+2)
Method #2
-
Let u=ex+2.
Then let du=exdx and substitute du:
∫u1du
-
The integral of u1 is log(u).
Now substitute u back in:
log(ex+2)
-
Now simplify:
log(ex+2)
-
Add the constant of integration:
log(ex+2)+constant
The answer is:
log(ex+2)+constant
The answer (Indefinite)
[src]
/
|
| x
| E / x\
| ------ dx = C + log\2 + E /
| x
| E + 2
|
/
∫ex+2exdx=C+log(ex+2)
The graph
−log(3)+log(2+e)
=
−log(3)+log(2+e)
Use the examples entering the upper and lower limits of integration.