finding value of indefinite integration of $\frac{y^7-y^5+y^3-y}{y^{10}+1}dy$ finding value of indefinite integration  $\displaystyle \int\frac{y^7-y^5+y^3-y}{y^{10}+1}dy$
$\displaystyle \int\frac{y^5(y^2-1)+y(y^2-1)}{y^{10}+1}dy = \int\frac{(y^5+y)(y^2-1)}{y^{10}+1}dy = \int\frac{(y^5+y)(y^2+1-2)}{y^{10}+1}dy$
$\displaystyle =\int\frac{y^5+y}{y^8-y^6+y^4-y^2+1}-2\int\frac{y^5+y}{y^{10}+1}dy$
i wan,t be able to proceed after that, could some help me with this

HINT: $$y^{10}+1= \left( {y}^{2}+1 \right)  \left( {y}^{8}-{y}^{6}+{y}^{4}-{y}^{2}+1
 \right) 
$$
further we get
$$\frac{y^7-y^5+y^3-y}{y^{10}+1}=1/5\,{\frac {y \left( 4\,{y}^{6}-3\,{y}^{4}+2\,{y}^{2}-1 \right) }{{y}
^{8}-{y}^{6}+{y}^{4}-{y}^{2}+1}}-4/5\,{\frac {y}{{y}^{2}+1}}
$$
