How to solve $$\int\frac{x^{9}}{1+x^{14}}\mathrm dx$$
I am trying this question by taking $x^{7} = u$ and then I am getting $7x^{6}\mathrm dx=\mathrm du$.
So, $x^{6}\mathrm dx=\frac{1}{7}\mathrm du$. Now $x^3$ will remain in the numerator and $x^3$ will be equal to $u^{\frac{3}{7}}$. So the final integral will be
$$\frac{1}{7}\int \frac{u^{\frac{3}{7}}}{1+u²}\mathrm du.$$
But how to approach further. Please help me out.