Question

What is the Indefinite integral of: (1)/(x*root(4(x^2)-1))

Answer 1

Do you have the answer on an answer sheet? I just need to check.

Answer 2

one second please

Answer 3

arctan of (1/root((4x^2)-1))

Answer 4

Unfortunately, I'm not as far as you into the topic of integration. Maybe someone else here can be more of an assistance to you. @hartnn

Answer 5

i was thinking of a u-substitution
4x^2 = sec u
so that root(4(x^2)-1) = root (sec^2 u-1) = tan u
but i am still working on it....donno whether it'll give us required answer.

Answer 6

***4x^2 = sec^2 u

Answer 7

the u should = root(4(x^2)-1) but i do not know what to do from there to solve

Answer 8

is it given/asked to ' u should = root(4(x^2)-1)' ??
because i don't see how that wil help...

Answer 9

i checked on wolframalpha same exact integral idk :/

Answer 10

thats how it solved it

Answer 11

let me try x=(sec u)/2
dx = sec u tan u /2

sec u tan u /(2 secu /2 * (tan u)) = 1
it works very nicely..

Answer 12

did u get that^ ?

Answer 13

let me try now =)

Answer 14

you could let u =

du = \[\frac{ 4x }{ \sqrt{4x^2 -1} }dx\]

= \[\int\limits_{}^{} 1 / (u^2 +1) du\]

= arctan(u) + C

Sub back for u

Answer 15

\(\large \int \dfrac{\sec u \tan u du }{2 (\sec u/2)(tan u)}=\int 1du=u+c\)

Answer 16

blurbendy what is your u ?

Answer 17

oh sorry,

u = \[\sqrt{4x^2 - 1}\]

Answer 18

so how did you end up substituting and canceling how did that u get you to the form of arctan ?

Answer 19

the roots end up cancelling

Answer 20

arctan is the anti-derivative of anything in the form:

1 / (x^2 + 1)

Just a rule of thumb basically.

Answer 21

4x doesnt equal 1

Answer 22

and it is not the derivative of 4x^2