Question

anti-derivative of ( 1/ (x sqrt(4x^2 -1)))dx
with the concept of http://prntscr.com/39apa9
Could someone please help me with this? :3

Answer 1

\[\large \int\limits_{}^{} \frac{ 1 }{ x \sqrt{4x^2-1} }\]

Answer 2

I was thinking u-sub u = 2x ?

Answer 3

What about u=4x^2-1 ?

Answer 4

we were on trig inverses topic

Answer 5

you don't need any substitution

Answer 6

put the x under the sqrt

Answer 7

Then you still need substitution?

Answer 8

not really

Answer 9

\[\int\limits_{}^{}\frac{ 1 }{ 4\sqrt{x^4-\frac{ x^2 }{ 4 }} }\]

Answer 10

anyways...
I did u = 2x
then du= 2dx
so multiply top and bottom by 2
and got arcsec2x
but textbook says 2arcsec2x
that is my problem

Answer 11

How did you get arcsec2x?

Answer 12

Do you know hyperbolics?