How can I simplify this complex integral involving a square root and fractions?

[mamou6262]

Homework Statement

Hello,
I have an equation which I am having to simplify.
$$\int \frac{1}{ x^2 \times \sqrt{a + bx^2 + \frac{c}{x^2}}} \,dx$$

2. The attempt at a solution
I've tried expanding the terms in the brackets and using a substitution of [ tex ] \[r=x^2\][ /tex ] but I need the answer in a form which is
$$\int \frac{1}{ \sqrt{d + ey + fy^2 }} \,dy$$
Thanks

 

[JesseC]

If I said:

$$\frac{1}{x^2 \sqrt{a+bx^2+\frac{c}{x^2}}} = \frac{1}{x \sqrt{ax^2+bx^4+c}}$$

Do you know how I got from one to the other?

There is a substitution you can use to get it in terms of y.

 

[zaf]

If you take
$$s = x^2$$.
Then,
$$ds = 2x$$
and replace in the substitution of JesseC right hand side.
Hope that helps.