Is this possible to integrate?

[jason17349]

Please help me integrate the following:

$$\int_0^x \frac{1}{\sqrt{(A+Bx^2+Cx^3+Dx^4)}} \,dx$$

I have no idea where to start or if this is even possible.

 

[StatusX]

I could be obnoxious, and say yes, just pull that big constant outside the integral, but I won't (or maybe I just did). But if you mean for those x's to be replaced by v's, then this integral is generally only possible if you can factor the denominator. Then you would proceed by the method of partial fractions, which you can look up in google to find an easy explanation of.

 

[mepcotterell]

maybe it's...

$$\frac{x}{\sqrt{(A+Bx^2+Cx^3+Dx^4)}}$$

 

[jason17349]

You are wrong on both counts, the dv is supposed to be dx

 

[StatusX]

I thought of that, but then you lose v altogether, which I figured you might want, and plus you'll have to change the limits of integration. It doesn't really matter.

 

[Hurkyl]

Of course it's integrable.

I'm 99.9% sure its not expressible in terms of "elementary" functions, though.

 

[StatusX]

Oh, was that square root always there? I must have missed it. Then, yes, no, you can't integrate it in general without resorting to elliptic itegrals and other messy functions.