5 x ( x)-2 d x= x+ | x-2 x|+ , then - =

Step-by-step solution

5 x x-2 d x= 5 x x-2 x d x Put, 5 x= ( x-2 x)+ array r d d x ( x-2 x) 5 x= ( x-2 x)+ ( x+2 x) array On comparison of coefficients of x, x we get x coefficients 5= +2 x coefficients 0=-2 + On solving Eqs. (i) and (ii), weget gathered =1 and =2 5 x=1( x-2 x)+2( x+2 x) gathered Now, substitute 5 x value in the given question. aligned & 5 x ( x-2 x) d x & = 1( x-2 x)+2( x+2 x) ( x-2 x) d x & = 1( x-2 x) x-2 x d x+2 x+2 x ( x-2 x) d x & = 1 d x+2 | x-2 x|+c & [ f^ (x) f(x) d x= |f(x)| ] & =x+2 | x-2 x|+c aligned On comp