# Integral question. Need help.

1. Sep 10, 2010

### Cepeda09

1. The problem statement, all variables and given/known data
What is the integral of (1)/(x sqrt(4x^4-9)) I need the steps. Thanks.

2. Relevant equations

3. The attempt at a solution

2. Sep 10, 2010

### jgens

What have you tried? No one here can give you any help until you've shown some attempt at the solution.

3. Sep 11, 2010

### Cepeda09

I first simplified it to the int of (1)/(x)(2x^2-3)
I also think that I have to use this, int (1)/(1+x^2) = arctan x +c, in order to solve it. But I can't figure it out.

4. Sep 11, 2010

### jgens

How did you simplify it like that?

I tackled this problem using a substitution, so I can help you if you're willing to work with that. There might be other ways, but I can't figure them out off the top of my head.

5. Sep 11, 2010

### pongo38

When you simplify something like (1)/(x sqrt(4x^4-9)) to (1)/(x)(2x^2-3), you should check it by putting in some value of x, say 1, to see if you have made an error in simplification. In this case what do you find when you do that?

6. Sep 11, 2010

### Cepeda09

I guess I did make a mistake because I am not getting the same thing. What do I need to do to solve it?

7. Sep 11, 2010

### Mentallic

A common mistake, but you need to lose this bad habit.

$$\sqrt{a^2+b^2}\neq a+b$$ because $$(a+b)^2=a^2+b^2+2ab\neq a^2+b^2$$

So you can't simplify the surd as you did.

8. Sep 11, 2010

### jgens

I solved it with a substitution. What substitution can you use to eliminate the squareroot in the denominator?

9. Sep 13, 2010

### pongo38

Whatever the substitution is, it could be based on the trig equation cos^2 x + sin^2 x = 1, or a similar thing. When this is rearranged as say cos^2 x = 1 - sin^2 x, you get something rather like your denominator. Can you work it from there?