s2/((s2+1)(s2+9)(s2+25))=A/(s2+1)+B/(s2+9)+C/(s2+25),
A(s2+9)(s2+25)+B(s2+1)(s2+25)+C(s2+1)(s2+9)=s2,
A(s4+34s2+225)+B(s4+26s2+25)+C(s4+10s2+9)=s2,
A+B+C=0, 34A+26B+10C=1, 225A+25B+9C=0;
C=-(A+B), 34A+26B-10A-10B=1, 24A+16B=1, 16B=1-24A;
225A+25B-9A-9B=0, 216A+16B=0⇒27A+2B=0.
-216A=1-24A, 1+192A=0, A=-1/192;
16B=1+24/192=9/8, B=9/128; C=-(-1/192+9/128)=-25/384.
s2/((s2+1)(s2+9)(s2+25))=(-1/192)(1/(s2+1))+(9/128)(1/(s2+9))-(25/384)(1/(s2+25)).
ℒ{cos(ωt)}=ω/(s2+ω2).
Expression becomes: -cos(t)/192+3cos(3t)/128-5cos(5t)/384.