I'm having problems with these 2 integrals and any help would be great.

$\displaystyle \int\frac{dx}{\sqrt{x^2-9}}$

here is my work

$\displaystyle x = 3\sec{\theta}$

$\displaystyle dx = 3\tan{\theta}\sec{\theta}$

plugging that in

$\displaystyle \int \frac{3\tan{\theta}\sec{\theta}d\theta}{3\tan{\the ta}}$

$\displaystyle \int \sec{\theta}d\theta$

$\displaystyle \ln{|\sec{\theta}+\tan{\theta}|}$

$\displaystyle \ln|\frac{x}{3} + \frac{\sqrt{x^2-9}}{3}| + C$

but the book has

$\displaystyle \ln|x+ \sqrt{x^2-9}| + C$

where did I go wrong?

The other problem is

$\displaystyle \int \frac{dx}{(4x^2-9)^3}$

I know I have to divide

$\displaystyle 4x^2-9$

by 4 to get

$\displaystyle x^2 - \frac{9}{4}$

but what do I divide the numerator by then, 64?

Thanks in advance