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calculus

posted by on .

Evaluate the integral of

xe^2x(dx)

A. (1/6)(x^2)(e^3x)+C

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

C. (1/2)(xe^2x)-(1/4)(e^2x)+C

D. (1/2)(x^2)-(1/8)(e^4x)+C

  • calculus - ,

    u dv = u v - int v du

    u = x
    du = dx

    dv = e^(2x) dx
    v = (1/2) e^(2x)
    so
    int x e^(2x) dx = (x/2)e^(2x)- int (1/2)e^(2x) dx

    = (x/2)e^(2x)- (1/4)e^(2x) +c
    so I think C.

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