# Integration help

1. Jun 13, 2010

### tweety1234

1. The problem statement, all variables and given/known data

Hi,

I am not sure if you can use a u-substitution on this integral, $$\int \frac{1}{\sqrt{9x^{2}+4}} dx$$?

$$\sqrt{9x^{2}+4}$$

Can I?

I have tried it, but get an even more complicated integral from what I started with.

2. Jun 13, 2010

### n.karthick

You can refer to the standard integrals in the PF library to get the solution directly.

3. Jun 13, 2010

### tweety1234

Thank you, but the table does not show me a method, and I would really like to know how to go about this.

I am right in saying we can use a substitution?

4. Jun 13, 2010

### Gib Z

You can use a substitution, but not the one you used. Have you learned the theory and method of trigonometric substitutions?

5. Jun 14, 2010

### n.karthick

Could you think of using the trigonometric relation $sin^2x+cos^2x=1$ to simplify your integral.

6. Jun 14, 2010

### HallsofIvy

Staff Emeritus
If that isn't a sufficient hint note that dividing both sides of $sin^2 x+ cos^2 x= 1$ by $cos^2 x$ gives $tan^2 x+ 1= sec^2 x$ and that
$$\sqrt{9x^2+ 4}= \sqrt{\frac{1}{4}\left(\frac{9x^2}{4}+ 1\right)}= \frac{1}{2}\sqrt{\left(\frac{3x}{2}\right)^2+ 1}$$