If (2 x+4) x-1 ~d x= a (x-1)^ 5 / 2 + b (x-1)^ 3 / 2 + c where c is a constant of integration, then the value of (2 a+b) is

Step-by-step solution

aligned & Let I= (2 x+4) x-1 d x & Let x-1= t & x=1+ t & ~d x= dt & I= [2(1+t)+4] t d t & = (6 t +2 t^ 3 2 ) d t & = 6 t ^ 3 2 3 2 +2 t ^ 5 2 5 2 + c & =4(x-1)^ 3 2 + 4 5 (x-1)^ 5 2 + c aligned Comparing with a (x-1)^ 5 2 + b (x-1)^ 3 2 + c , we get array cl & a= 4 5 , b=4 & 2 a+b= 8 5 +4= 28 5 array