Integration using Table of integrals?

Integrate ( e^x ) dx / (3-e^2x) I'm stumped...

Question

Integration using Table of integrals? 

Integrate ( e^x ) dx / (3-e^2x)  I'm stumped...

helder_edwin · Answer

$$ \large \int\frac{e^x}{3-e^{2x}}\,dx $$
?

anonymous · Answer

yep.

anonymous · Answer

on my table of integrals, I thought maybe using the int du/ u sqrt( a +bu) would work but idk how to set it up

helder_edwin · Answer

u already learned substitution, right?

anonymous · Answer

u sub yes...
but im not sure for this one...

anonymous · Answer

we have to use the table of integrals...

helder_edwin · Answer

u use substitution in order to turn an integral that is not on the table into one that IS on the table.

helder_edwin · Answer

u can rewrite the integral into
$$ \large \int\frac{e^x}{3-(e^x)^2}\,dx $$
right?

anonymous · Answer

yes

anonymous · Answer

so u would be e^x

anonymous · Answer

du is e^x as well?

helder_edwin · Answer

yes

helder_edwin · Answer

so if u=e^x then du=e^x dx therefore the integral becomes
$$ \large \int\frac{1}{3-u^2}\,du $$
agree?

helder_edwin · Answer

this one should be on your table. right?

anonymous · Answer

im looking...

helder_edwin · Answer

i have it. do u want me to post it?

anonymous · Answer

please

anonymous · Answer

theres too many agh!

helder_edwin · Answer

no problem
$$ \large \color{blue}{\int\frac{dx}{a^2-x^2}=\frac{1}{2a}\ln
    \left|\frac{a+x}{a-x}\right|+C} $$
for $a\neq0$

anonymous · Answer

thank you so much!!!!

helder_edwin · Answer

compare with what we got
$$ \large \int\frac{1}{3-u^2}\,du $$
a^2=.....

anonymous · Answer

did you get this from a table? what number was it? i cant find this one in my table... but its definetly the right one i just cant find it

helder_edwin · Answer

we must have different tables. i have a russian book with me.

helder_edwin · Answer

what is the value of a^2 ?

anonymous · Answer

i see... ill keep looking..

anonymous · Answer

found it!

anonymous · Answer

I have another question regarding these integrals using the tables. could you help?

anonymous · Answer

ill post a new question so you get credit

helder_edwin · Answer

sure. but, shouldn't we first finish this one?

anonymous · Answer

i finished it i just needed to find the formula from the tables... a is sqrt 3 and then you simply plug the rest in right?

helder_edwin · Answer

and replace the value of u=e^x

anonymous · Answer

yes.

helder_edwin · Answer

ok.

anonymous · Answer

i will close this and open a new question..