# Thread: finding the indefinite integral

1. ## finding the indefinite integral

∫▒〖1/(3-9x^2 ) dx〗

i know this problem is not hard but im not getting what the back of the book is getting.

the directions told me to use this formula:

∫▒〖du/(a^2-u^2 ) 〗= 1/2a ln (a+u)/(a-u)+ C

note: there should be absolute bars around the ln quantity i dont know how to make those on my computer. this problem seems easy enough. simple substitution and then solve it, but im not getting it. any help would be appreciated. thanks in advance.

2. Originally Posted by slapmaxwell1
∫▒〖1/(3-9x^2 ) dx〗

i know this problem is not hard but im not getting what the back of the book is getting.

the directions told me to use this formula:

∫▒〖du/(a^2-u^2 ) 〗= 1/2a ln (a+u)/(a-u)+ C

note: there should be absolute bars around the ln quantity i dont know how to make those on my computer. this problem seems easy enough. simple substitution and then solve it, but im not getting it. any help would be appreciated. thanks in advance.
$\frac{1}{3 - 9x^2} = \frac{1}{(\sqrt{3})^2 - (3x)^2}$

let $u = 3x$, then $du = 3dx$

3. ## ok

ok see thats what i did, i simply plugged and chugged and i didnt get what the back of the book had, which was really weird. it was close but not quite the same. i thought maybe i missed something, perhaps a step or something. because at first glance the problem appears to be very easy, but i will re work it and try to post my work. thx

4. ## solve like this (with formula)

solve like this as dedust poseted

and use this formula 1/(a^2-x^2) dx =(1/2a)log|a+x/a-x|+c

were a is constant and x is variable.
substitute your values in above formula.

when u try to solve at the end of problem you will also use formulas like:-
log|m/n|=logm/logn and also

log|mn|= logm+logn
i dont what answer is given in your text book, when u try to solve it u will know
where to end the problem,

5. Originally Posted by avengerevenge
solve like this as dedust poseted

and use this formula 1/(a^2-x^2) dx =(1/2a)log|a+x/a-x|+c

were a is constant and x is variable.
substitute your values in above formula.

when u try to solve at the end of problem you will also use formulas like:-
log|m/n|=logm/logn and also

log|mn|= logm+logn
i dont what answer is given in your text book, when u try to solve it u will know
where to end the problem,
thanks i got the right answer, now its time to study for the exam, its kinda cool we are getting ready to start a little diffy in calc II! awesome!