Evaluate β« xe2x dx. A. 1/6x2 e3x + CB. 1/2xe2x - 1/2 xe2x + CC. 1/2xe2x - 1/4 e2x + CD. 1/2x2 - 1/8 e4x + C
Accepted Solution
A:
The formula is integral of (udv) = uv - integral of (vdu) We use integration by parts by letting u = x and dv = (e^2x)dx Then du = dx, and v = (1/2)(e^2x) integral of x(e^2x)dx = (1/2)(x)(e^2x) - integral of (1/2)(e^2x)dx = (1/2)(x)(e^2x) - (1/4)(e^2x) + C Therefore the correct answer is C.