# Evaluate this integral

1. Jun 25, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
$\displaystyle \int^∞_0 \dfrac{dx}{a^2 + \left(x-\frac{1}{x} \right)^2}$ a>=2

3. The attempt at a solution

$\displaystyle \int^∞_0 \dfrac{x^2 dx}{x^2a^2 + (x^2-1)^2}$

2. Jun 25, 2013

### Pranav-Arora

Put $\displaystyle x=\frac{1}{t}$ in the given integral.

3. Jun 26, 2013

### sankalpmittal

Not sure about Pranav's hint but here is how I would have done it:

Making a tricky substitution of,

1/t = x-1/x

OR

In your attempt at solution, expand the denominator, then write numerator as x2-1+1, break the denominator, then in each integrand, divide both sides by x2, try making the denominator the perfect square, then in term like Y2 in the denominator, let Y=t...etc..