If 729 ₁^3 1 x^3 (x^2+9 )^2 d x=a+ b , then a-b=

Step-by-step solution

I =729 ₁^3 1 x^3 (x^2+9 )^2 d x Let 1 x^3 (x^2+9 )^2 = A x + B x^2 + C x^3 + D x+ E x^2+9 + F x+ G (x^2+9 )^2 aligned & 1=x^3 (x^2+9 )( D x+ E )+x^3( ~F x+ G ) & +x^2 (x^2+9 )^2 ~A +x (x^2+9 )^2 ~B + (x^2+9 )^2 C & 1=x^6( ~A + D )+x^5( ~B + E )+x^4(18 ~A + C +9 D + F ) & +x^3(18 ~B +9 E + G )+x^2(81 ~A +18 C )+81 x ~B +81 C aligned On comparing, aligned & A + D =0, ~B + E =0 ; 18 ~A + C +9 D + F =0 & 18 ~B +9 E + G =0,81 ~A +18 C =0 & 81 ~B =0,81 C =1 & ~A = -2 729 , B=0, C= 1 81 , D= 2 729 , E=0, F= 1 81 & G =0 &