Integration of $1/(x^4 \sin x +2x)$ $$\int\frac{1}{x^4 \sin x +2x} dx\ $$  How to evaluate this integral. How to go about evaluating these integrals?

Hint:
$\int\dfrac{1}{x^4\sin x+2x}dx$
$=\int\dfrac{1}{2x\left(1+\dfrac{x^3\sin x}{2}\right)}dx$
$=\int\sum\limits_{n=0}^\infty\dfrac{(-1)^nx^{3n-1}\sin^nx}{2^{n+1}}dx$
$=\int\left(\dfrac{1}{2x}+\sum\limits_{n=1}^\infty\dfrac{(-1)^nx^{3n-1}\sin^nx}{2^{n+1}}\right)dx$
But this approach is only suitable for the very limited ranges of $x$ : $\left|\dfrac{x^3\sin x}{2}\right|\leq1$
