Integration help

Homework Statement

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.

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

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

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?

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

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

HallsofIvy
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
$$\sqrt{9x^2+ 4}= \sqrt{\frac{1}{4}\left(\frac{9x^2}{4}+ 1\right)}= \frac{1}{2}\sqrt{\left(\frac{3x}{2}\right)^2+ 1}$$