_ x 2 x- x ( -2 x)^3 equals

Step-by-step solution

aligned Let I & = _ x 2 x- x ( -2 x)^3 & = _ x 2 x(1- x) x( -2 x)^3 Put x & = 2 - h -2 x & =2 ~h As x & 2 , ~h 0 aligned aligned I & = _ h 0 ( 2 -h ) (1- ( 2 -h ) ) ( 2 -h )(2 h)^3 & = _ h 0 h 2 ^2 ( h 2 ) 8 h^3 & = 2 8 _ h 0 h h _ h 0 ^2 h 2 h^2 4 4 & = 2 8 (1) (1) 1 4 & = 1 16 aligned