Let X be a randon variable with density function:

$\displaystyle f(x) = \frac {cx^6}{1+7x^{20}} \ \ \ \ \ -1 \leq x \leq 1 $

and $\displaystyle f(x) = 0 \ \ \ otherwise $

where c is such that this is a density.

Find $\displaystyle E[X]$

First I tried to take the integral of $\displaystyle \int _{-1}^{1} \frac {cx^6}{1+7x^{20}} = 1 $ to find c, but I'm stuck here unless I get to use a calculator.

Are there anyway to find c? Or rather, do I need to find c in order to find the expected value, that is, $\displaystyle \int _{-1}^{1} \frac {cx^7}{1+7x^{20}} $