Solving a Difficult Integral: Strategies and Advice

[dirk_mec1]

Homework Statement

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

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?

 

[MadHawk]

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.

 

[Unco]

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.

That's a degree 16 polynomial, there MadHawk.

Homework Statement

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

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?

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.

 

[gabbagabbahey]

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.

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!

 

[gabbagabbahey]

Homework Statement

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

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?

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

 

[MadHawk]

Well, it was just pure innocent fun. The actual quantity under root is (x^2+5)^2 - 96(x+1). From here, I think, it can be done. Sorry folks, for the joke above.

 

[dirk_mec1]

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

Yes, this IS the correct integral. Furthermore there is an exact solution which can be written in elementary functions. What can you advice me to do? Is Madhawks suggestion the way to tackle this integral?

Where are Dick and HallsofIvy? Or did I scare them away