# Integration Using Hyperbolic Identities

• Apr 23rd 2011, 04:45 AM
Mcoolta
Integration Using Hyperbolic Identities
So i need to solve:

The integral of 1/ Sqrt( 9x^2 - 16) dx

If the 9 wasnt infront of x^2, i could easily do it, letting x = 4cosh(u) and so on, but the 9 confuses me.

Am i right in thinking i take a 9 out, to leave :

1/ sqrt( 9(x^2 - 16/9) ) dx and then: (1/3) * Integral of 1/ sqrt(x^2 - 16/9) dx?

As when i tried this, i got the incorrect answer.

Also, apologies if the format is difficult to understand, i tried to use latex, but got ' Latex Error: Compile failed'

Thanks
• Apr 23rd 2011, 05:15 AM
topsquark
Quote:

Originally Posted by Mcoolta
So i need to solve:

The integral of 1/ Sqrt( 9x^2 - 16) dx

If the 9 wasnt infront of x^2, i could easily do it, letting x = 4cosh(u) and so on, but the 9 confuses me.

Am i right in thinking i take a 9 out, to leave :

1/ sqrt( 9(x^2 - 16/9) ) dx and then: (1/3) * Integral of 1/ sqrt(x^2 - 16/9) dx?

So far so good. Now make the substitution x = sqrt(16/9)*cosh(u) = (4/3)*cosh(u). This gives dx = (4/3)*sinh(u) du, so the integral becomes
http://latex.codecogs.com/png.latex?...osh^2(u) - 1}}

http://latex.codecogs.com/png.latex?...osh^2(u) - 1}}

Can you take it from here?

-Dan