$$\int\_{0}^{1} \frac{e^x}{x^6+x} dx$$

This how i approached the problem:

1st Step : Using partial fractions.
$$e^x = A(x^5+1)+Bx^2+Cx$$

Now can i solve for $$Cx = e^x$$ and get $$C=e^{-ln(x)+x}$$

I want to understand if these are special kind of problem while, i dont think $$x^6+x)$$ is a polynomial that i could just factor. If someone has time and Energy to show me how it is done. Would highly appreciate it.