For x>0 , if ( x)^5 d x is equal to x [A( x)^5+ . .B( x)^4+C( x)^3+D( x)^2+E( x)+F ]+ constant, then A+B+C+D+E+F is equal to

Step-by-step solution

Given that, aligned ( x^2 ) d x & =x [A( x)^5+B( x)^4 ] & .+C( x)^3+D( x)^2+E( x)+F ]+C aligned Let I= ( x)^5 d x Put x=t x=e^t d x=e^t d tI= t^5 e^5 d tI=e^t [t^5-5 t^4+20 t^3-60 t^2+120 t-120 ]+C Now, put E = x aligned & I=x [( x)^5-5( x)^4+20( x)^3-60( x)^2+120 . & ( x)-120]+C & A+B+C+D+E+F & =1-5+20-60+120-120=-44 & aligned