# Integrate in Mathematica takes forever

I'm trying to calculate the length of a curve from a polynomial in Mathematica and for some reason Integrate doesn't complete, it just runs until I abort the execution.

The polynom:

58.1735 - 36.4175 x + 7.10945 x^2 - 0.538311 x^3 + 0.0138115 x^4


Is a part of an integration like this:

where "koordfitprim" is the polynom above (i.e. what is integrated is in fact the square root of 1 + the above polynom^2).

Any ideas why this wouldn't execute?

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I assume that the polynomial you quote is the derivative of the polynomial $P(x)$ such that the curve you are trying to find the length of (part of) has equation $y=P(x)$. – André Nicolas May 19 '11 at 22:37
@user6312 yes it is. My first attempt was integrating and deriving all at the same time but as it took forever, I started taking stuff out to see if I could find what was slowing things down. – Kalle May 20 '11 at 10:48

You should try to use NIntegrate (instead of Integrate). Integrate is for symbolic integration. NIntegrate for numerical integration. So try

NIntegrate[Sqrt[1+koordfitprim^2],{x,3,18}]

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Ohh, I see. Thank you! Wow, that instantly equated. THANK YOU!! – Kalle May 19 '11 at 20:45

This is a very tough integral and you asked Mathematica to evaluate it symbolically i.e. analytically. I am not sure whether it can be calculated at all.

What you wanted was a numerical integral

NIntegrate[Sqrt[1 + ko[x]^2], {x, 3, 18}]

The result is, after a fraction of a second,

59.211531

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What fraction of a second was it... 13/4 ?? – The Chaz 2.0 May 19 '11 at 20:53