1. ## Intergration help

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

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

here is my work

$x = 3\sec{\theta}$

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

plugging that in

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

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

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

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

but the book has

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

where did I go wrong?

The other problem is

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

I know I have to divide

$4x^2-9$

by 4 to get

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

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

2. ## Re: integration help

Hi,
I can't figure out what is going on with the first integral. I plugged it into Wolfram Alpha which gives an alternative answer which is quite confusing.

However with your second one yes, simply divide the numerator/ whole integral by 64.

3. I solved the first problem and got the same answer you did. I used Wolfram Mathematica to confirm it, and your answer is correct. I guess the book answer is wrong.

Patrick

4. ok thanks but I'm still having problems on the last problem

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

$\int \frac{\frac{dx}{64}}{(x^2-\frac{9}{4})^3}$

$x = \frac{2}{3}\sec{\theta}$

$dx = \frac{2}{3}\sec{\theta}\tan{\theta}$

plugging all that in I get

$\frac{2}{2187} \int \frac{\sec{\theta}\tan{\theta}d\theta}{\tan^6{\the ta}}$

and this is where I get stuck. Could someone check my work and show me how to solve it? Thanks in advance.

5. Originally Posted by PatrickFoster
I solved the first problem and got the same answer you did. I used Wolfram Mathematica to confirm it, and your answer is correct. I guess the book answer is wrong.

Patrick
I figured out what the book did.

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

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

they just combine the constant of ln3 with the constant.