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

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In summary, the conversation is about simplifying an equation involving an integral with a fraction and a square root. The person has attempted to solve it by expanding terms and using a substitution, but needs help to get the answer in a different form. They are instructed to use a substitution of s=x^2 to simplify the equation.
  • #1
mamou6262
2
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Homework Statement



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

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
[tex]
\int \frac{1}{ \sqrt{d + ey + fy^2 }} \,dy
[/tex]
Thanks
 
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  • #2
If I said:

[tex]\frac{1}{x^2 \sqrt{a+bx^2+\frac{c}{x^2}}} = \frac{1}{x \sqrt{ax^2+bx^4+c}}[/tex]

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.
 
  • #3
If you take
[tex] s = x^2 [/tex].
Then,
[tex] ds = 2x [/tex]
and replace in the substitution of JesseC right hand side.
Hope that helps.
 

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