Whats the name of this function?

[granpa]

this site:
http://integrals.wolfram.com
gives the integral of this function:


((2.5e+9)*x^5.5)/(((1.25e+10)-x)*(1e55))

but the answer contains some function I've never heard of before and can't find in the documentation.

it looks like ₂F₁ (6.5, 1; 7.5; 8.02014*10^-11x)

whats the name of this function?

 

[chislam]

Well right at the bottom of the page that gives the anti-derivative, you have two links to the function named Hypergeometric2F1 (Hypergeometric Function).

 

[uart]

Good site.

I just tried $$\int \frac{x^{11/2}}{1-x}$$ and I got a result in terms of only standard functions (just log sqrt and polymonials).

Your integral can easily be put in the above form with a change of variable so I'm not sure why you got a Hypergeometric?BTW. The result I got was :

$$\frac{-2 \sqrt{x} \, (3465 + 1155 x + 693 x^2 + 495 x^3 + 385 x^4 + 315 x^5 )} {3465}\, - \, \log(-1 + \sqrt{x}) \,+\, \log(1 + \sqrt{x})$$Note that I entered your integral (or one trivially close to it) in the form that I thought would be least likely to confuse the program. I find that this is usually a good idea if you're hoping to get an answer in it's simplest form.

BTW. Just substitute x = 1.25E+10 u to put your itegral into the above form.

 

[uart]

BTW: I just checked and it was only the 11/2 versus the 5.5 that was needed to give the simpler result.Also it seems that there's plenty of factors that cancel in the above.
$$-2 \sqrt{x} \, (1 \,+\, \frac{1}{3}\, x \,+\, \frac{1}{5}\, x^2 \,+\, \frac{1}{7}\, x^3 \, +\, \frac{1}{9}\, x^4 \, +\, \frac{1}{11} x^5 ) - \, \log(-1 + \sqrt{x}) \,+\, \log(1 + \sqrt{x})$$