SOLUTION: I need some help with integrals. Here is one a do not get: intergral of (e^x)/(1+e^x)^2 with the min 0 and max 2

Question 132348: I need some help with integrals. Here is one a do not get: intergral of (e^x)/(1+e^x)^2 with the min 0 and max 2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
intergral of (e^x)/(1+e^x)^2 with the min 0 and max 2integral of
(e^x)/(1+e^x)^2 with the min 0 and max 2
-------------------------
If you are using "u" substitution:
Let u = 1+e^x
Then du = e^x dx
------------------------
Swithching to the u variable you have:
So Integral (1+e^x)-2*e^x dx
= integral u^-2du
= -u^-1
--------------
Substituting back to the x variable you have:
= -(1+e^x)^-1 evaluated form x= 0 to x = 2
= [-(1+e^2)^-1] - [-(1+e^0)^-1]
= [-1/(1+e^2)] + (1/2)
= [-2+1+e^2]/2(1+e^2)
= [-1+e^2]/[2(1+e^2)]
=========================
Cheers,
Stan H.

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