Logarithmic Integral Homework: Solving S [(e^x)(e^x)]/((2+(e^x))^2) dx

[ppkjref]

Homework Statement

S = integral symbol
S (e^(2x))/((2+(e^x))^2) dx

Homework Equations

u = 2+(e^x)
(e^x) = u-2
du = (e^x) dx

The Attempt at a Solution

S [(e^x)(e^x)]/((2+(e^x))^2) dx
S [du(u-2)]/(u^2)
For the first (e^x) dx I substituted du. And since there was only (e^x) left, I substituted in u-2.
Now what do I do?
I know how to do du/(u^2). but what about the (u-2)?

 

[Gib Z]

So you need to find $$\int \frac{u-2}{u^2} du$$ . Just split the numerator like this: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$.

 

[ppkjref]

the a/c fraction is u/(u^2), equivalent to 1/u which when integrated is 0?

 

[Gib Z]

$$\int \frac{1}{u} du = \log_e u$$.

You should be familiar with that already.

 

[ppkjref]

ln(2+(e^x) + 2/(2+(e^x))
Just needed a break I guess. Wasn't thinking.

 

[Char. Limit]

ln(2+(e^x)) + 2/(2+(e^x))
Just needed a break I guess. Wasn't thinking.

An unmatched left parentheses can haunt you all day.