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: put $u = y^2$, and note that $(y^5 + y)dy = y(y^4+1)dy = \dfrac{u^2+1}{2}du$. Would this enable you to continue?
