# Very difficult integral

1. Jan 8, 2009

### dirk_mec1

1. The problem statement, all variables and given/known data

$$\int \frac{x}{\sqrt{x^4 + 10 x^2 - 96 x - 71}}\ \mbox{d}x$$

3. The attempt at a solution
I don't see what's useful completing a square, gonio substitution (or even a useful substitution). Does anyone have an idea?

2. Jan 8, 2009

The denominator can be replaced as [{(x^2+5)^2/96 - 1}^2 + 5]^2.

P.S. That /96 is to the whole (x^2+5)^2 expression.

3. Jan 8, 2009

### Unco

That's a degree 16 polynomial, there MadHawk.

Was this a homework problem, Dirk? Could you provide some context as to where it arose. According to the integrator at http://integrals.wolfram.com/index.jsp?expr=x/Sqrt[x^4+10*x^2-96*x-71]&random=false, it would seem the integral as you have written it cannot be expressed in elementary terms.

4. Jan 8, 2009

### gabbagabbahey

Your expression isn't even of the same degree as the denominator in the original expression

I think you'd better double check your math on that one!

5. Jan 8, 2009

### gabbagabbahey

Hmmm... are you sure that $-96x$ is supposed to be there?

6. Jan 8, 2009