# Integral of polynomial to some power

1. Jul 30, 2009

### Wiemster

Does anybody know in general how (if) one can perform the integral of a general polynomial to some, not necessarily integer, power? I.e.

$$\int \left(\Sigma_{i=0} ^n c_i x^i \right)^a dx$$

with $c_i$ and $a$arbitrary (real) numbers,

$$\int \left(1+x + x^2 + 2x^5 \right)^{1.7} dx$$.

Maybe what I'm looking for is some generalization of Newton's binomium?

2. Jul 30, 2009

### HallsofIvy

Staff Emeritus
There is no simple way to do that.

3. Jul 30, 2009

### Wiemster

I already thought it would be difficult, if not impossible. Too bad. Thanks anyway.

4. Jul 30, 2009

### g_edgar

$\int\sqrt{\text{fourth degree}}$ = elliptic integral

$\int_0^1 [x(1-x)]^a\,dx$ = Beta function