If x^3 e^ 2 x d x= e^ 2 x 8 f(x)+c , then the sum of all the complex roots of f(x)=1 is

Step-by-step solution

Given, x^3 e^ 2 x d x= e^ 2 x 8 f(x)+c By applying integration by parts, we get aligned & .x^3 e^ 2 x d x- ( d d x x^3 e^ 2 x d x ) d x )= e^ 2 x 8 +f(x)+c & x^3 e^ 2 x 2 - 3 x^2 e^ 2 x 2 d x= e^ 2 x 8 f(x)+c & 1 2 x^3 e^ 2 x - 3 2 [x^2 e^ 2 x 2 - 2 x e^ 2 x 2 d x ]= e^ 2 x 8 f(x)+c aligned [Again applying integration by parts] array r 1 2 x^3 e^ 2 x - 3 4 x^2 e^ 2 x + 3 2 x e^ 2 x d x= e^ 2 x 8 f(x)+c 1 2 x^3 e^ 2 x - 3 4 x^2 e^ 2 x + 3 2 [x e^ 2 x 2 - 1 e^ 2 x 2 d x ] = e^ 2 x 8 f(x)+c array aligned & 1 2 x^3 e^