and so I was trying to do some practice trig anti derivatives and now my head's spinning ,

Question

and so I was trying to do some practice trig anti derivatives and now my head's spinning >,<
a little help pwease? :3

$$\large \int\limits \frac{ dx }{ 1 + e^x } $$

jigglypuff314 · Answer

Here's what I've tried doing do far
$$\rightarrow \int\limits \frac{(e^{x/2}-e^{x/2}+1)}{1+e^x}dx~\rightarrow \int\limits \frac{e^{x/2}}{1+e^x}dx- \int\limits \frac{e^{x/2}}{1+e^x}dx+ \int\limits \frac{1}{1+e^x}dx$$

parthkohli · Answer

I haven't studied integration that deeply, but from what you've done so far, you're ending up with the same integral in the end.

jigglypuff314 · Answer

I was just trying to find a way to use a trig integral :/
cuz the $$\int\limits \frac{e^{x/2}}{1+e^x}dx \rightarrow \int\limits \frac{e^{x/2}}{(1)^2+(e^{x/2})^2}dx$$

parthkohli · Answer

Yeah, I see that, but we still don't have a way to compute the last term. But well - both of us know that and I haven't added anything significant so far. Heh.

jigglypuff314 · Answer

which is why I'm stuck >,<

turingtest · Answer

tan(u)=e^(x/2) ?

jigglypuff314 · Answer

mmm?
I yeah I was thinking  u = e^(x/2)

turingtest · Answer

oh i see that is not where you are stuck

turingtest · Answer

parth is right that the last term will mess us up

jigglypuff314 · Answer

so to try another way entirely?

turingtest · Answer

yeah

turingtest · Answer

im super rusty lol, I have to remember how to do this

jigglypuff314 · Answer

my math teacher hinted about adding and subtracting something to the numerator to make it work
but the wolframalpha solution doesn't do that and it confusing me >,<

turingtest · Answer

add and subtract e^x in the  numerator
no trig needed

parthkohli · Answer

Ooo, how did I not think of that?

jigglypuff314 · Answer

$$\int\limits \frac{e^x-e^x+1}{1+e^x}dx$$? then...?

jigglypuff314 · Answer

oh if u = e^x
then du = e^x dx

parthkohli · Answer

$e^x$ and $1-e^x$ are to be separated.

parthkohli · Answer

yeah, then a sub.

jigglypuff314 · Answer

what do I do with the$$\int\limits \frac{1-e^x}{1+e^x}$$

turingtest · Answer

other way fellas
1+e^x and -e^x need to be separated

jigglypuff314 · Answer

*facedesk* I see now xD

parthkohli · Answer

Oh, crap. The effects of sleep-deprivation are showing up early (or late?)

turingtest · Answer

It happens to the best of us... and also to me :P

jigglypuff314 · Answer

Thanks for your help! @TuringTest @ParthKohli ^_^

parthkohli · Answer

Alright, bring 'em on.

parthkohli · Answer

The integrals, I mean. Can't play the sidekick anymore. :|