_ 2 ^ x - x x x(x + x) , dx equals

Step-by-step solution

Let I = _ 2 ^ x - x x x(x + x) , dx Adding and subtracting x in the numerator, we get: I = _ 2 ^ x + x - x - x x x(x + x) , dx I = _ 2 ^ (x + x) - x(1 + x) x(x + x) , dx Separating the terms, we obtain: I = _ 2 ^ ( x + x x(x + x) - x(1 + x) x(x + x) ) , dx I = _ 2 ^ ( 1 x - 1 + x x + x ) , dx Integrating each term with respect to x : I = [ x - (x + x) ]_ 2 ^ I = [ ( x x + x ) ]_ 2 ^ Substituting the upper and lower limits: I = ( + ) - ( 2 2 + 2 ) Since = 0 and 2 = 1 : I = ( + 0 ) - ( 2 2 + 1 ) I = (1) - ( + 2 ) I =