5 x x-2 ~d x=x+ a | x-2 x|+ c (where c is a constant of integration), then the value of a is

Step-by-step solution

Let aligned I & = 5 x x-2 ~d x & = 5 x x-2 x ~d x aligned Let 5 x= A ( x-2 x)+ B d d x ( x-2 x) aligned & 5 x= A ( x-2 x)+ B ( x+2 x) & A +2 ~B =5 and -2 ~A + B =0 aligned Solving these equations, we get aligned A & =1, ~B =2 I & = 1 ~d x+2 x+2 x x-2 x ~d x & =x+2 | x-2 x|+ c aligned But 5 x x-2 ~d x=x+ alog | x-2 x|+ c Comparing, we get a =2