Ask Question
25 November, 18:21

Evaluate ∫ xe2x dx. 1 2 3x A./xe + C 6 B. 1/xe2x-1 / xe2x+C 22 C. 1/xe2x-1 / e2x+C 24 1 2 1 4x D./x-/e + C 28

+4
Answers (1)
  1. 25 November, 21:32
    0
    The answer is (1/2) xe^ (2x) - (1/4) e^ (2x) + C

    Solution:

    Since our given integrand is the product of the functions x and e^ (2x), we can use the formula for integration by parts by choosing

    u = x

    dv/dx = e^ (2x)

    By differentiating u, we get

    du/dx = 1

    By integrating dv/dx = e^ (2x), we have

    v = ∫e^ (2x) dx = (1/2) e^ (2x)

    Then we substitute these values to the integration by parts formula:

    ∫ u (dv/dx) dx = uv - ∫ v (du/dx) dx

    ∫ x e^ (2x) dx = (x) (1/2) e^ (2x) - ∫ ((1/2) e^ (2x)) (1) dx

    = (1/2) xe^ (2x) - (1/2) ∫[e^ (2x) ] dx

    = (1/2) xe^ (2x) - (1/2) (1/2) e^ (2x) + C

    where c is the constant of integration.

    Therefore,

    ∫ x e^ (2x) dx = (1/2) xe^ (2x) - (1/4) e^ (2x) + C
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Evaluate ∫ xe2x dx. 1 2 3x A./xe + C 6 B. 1/xe2x-1 / xe2x+C 22 C. 1/xe2x-1 / e2x+C 24 1 2 1 4x D./x-/e + C 28 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers