Homework Soursehow do I integrate x2e2xSolution int x2 e2x dx integrate by
how do I integrate x^2e^-2x
Solution
int( x^2 e^-(2x) dx integrate by parts u = x^2 du = 2x dx v = e^-(2x) dx d v = (-1/2)e^-(2x) ? x^2 e^-(2x) dx = (-1/2) x^2 e^-(2x) - ? x e^-(2x) dx again integrate x e^-(2x) dx by parts u = x : du = dx v = e^(-2x) dx : dv = (1/2) e^(-2x) x^2 e^-(2x) dx = (-1/2) x^2 e^-(2x) +[ (1/2) x e^(-2x) +1/2 ? e^(-2x) dx ] = (-1/2) x^2 e^(-2x) - (-1/2) x e^(-2x) -1/2 ? e^(-2x) dx = (-1/2) x^2 e^(-2x) + (1/2) x e^(-2x) -(1/4)e^(-2x) + C = (-1/4) e^(-2x) [ 2x^2 - 2x + 1 ] + C
