Need help with integration by substitution for 9X^4 + 9X^2?

[superkam]

Homework Statement

Hi, I'm having trouble with the following problem:

$$\int \sqrt{9X^4 + 9X^2}$$

Homework Equations

Integration by substitution? U = some form of X

The Attempt at a Solution

Hi,
I assume that the best way to solve this integral is by using some sort of substitution, the problem is I don't exactly know what the substitute. I've tried the obvious option;$$U = 9X^4 + 9X^2$$ but didn't really get anywhere.
If anyone could give me any clues on what substitution to use I would really appreciate it.
Thanks in advance

Kam

 

[Dickfore]

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

Then, you can either do the trigonometric substitution:

$$x = \tan{t}$$

or the hyperbolic substitution:

$$x = \sinh{t}$$

 

[Sourabh N]

x^2 + 1 = t also works well.

 

[superkam]

Okay, thank you very much for your help :)