Evaluate the following integral:
1/([e^-x] +2) dx

Question

Evaluate the following integral: 
1/([e^-x] +2) dx

anonymous · Answer

I know I need to multiply by a special  of (e^x/e^x) but from there I get shakey

myininaya · Answer

multiply top and bottom by e^x
then let u=1+2e^x

myininaya · Answer

$$\int\limits_{}^{}\frac{e^x}{1+2e^x} dx$$

myininaya · Answer

$$u=1+2e^x=>du=2e^x dx =>\frac{1}{2}du=e^x dx$$

anonymous · Answer

really?  i am impressed

myininaya · Answer

$$\int\limits_{}^{}\frac{1}{2} \frac{du}{u}$$

anonymous · Answer

learn something new every day!

myininaya · Answer

$$\frac{1}{2} \ln|u|+C=\frac{1}{2}\ln(1+2e^x) +C$$

anonymous · Answer

I messed up on my u. Ahhhhh. That's what happened.

anonymous · Answer

Thanks for the  clearly defined steps, I really appreciated it. : )

myininaya · Answer

np

myininaya · Answer

is this section on hyperbolic trig functions?

myininaya · Answer

it seems some cal classes do not cover hyperbolic trig functions

anonymous · Answer

I just been taught hyperbolic trig this semester. You're right though t semester I took Calc 2, it wasn't taught.

anonymous · Answer

*last

myininaya · Answer

i guess it depends on the instructor.
my instructor do not cover it either.

myininaya · Answer

but you sort of don't need to cover it i think

myininaya · Answer

its just using algebra tricks

anonymous · Answer

especially since they are usually covered in a 
'here's the definition, and here are a couple properties" fashion

anonymous · Answer

I like hyperbolic trig functions. If you're familiarwith your basic integration techniques then it's not too bad.

anonymous · Answer

The 1st time I took Calc2 it was presented as "here's the definition" and then bam expected to know how to do them. It sucked.

anonymous · Answer