Consider the differential operator

L$=((8$x$^2+4)$x$)$d$/$dx$+(1/4(1+$x$^2)^2)$

d$^2/$dx$^2$

acting on functions defined on the interval$[1,1].$

Find the function $($x$)$ such that L:$=$L is in Sturm$-$Liouville form:

L$=$d$/$dx$($p$($x$)$d$/$dx$)$

i$.$e$.$ find the necessary integrating factor. Why is exp$(8/($x$^2+1))*($x$^2+1)^16$ the wrong answer?