What is the integration of xe^2x?

I'm assuming you know how to use integration by parts. If you don't... good luck. Anyways, using dv=e^2x and u=x (and S is used for the symbol of integration)
v = 1/2 e^2x ; dv =e^2x dx
u=x ; du=dx

1/2 xe^2x - S(1/2e^2x dx) =
1/2 xe^2x - 1/4 e^2x

I knew to use integration by parts because you can see that there are two different functions in the problem: the e^x function and then simply the polynomial function. When there's two different types multiplied by each other, you will typically use integration by parts.

Integrate by parts, with u = x & dv = e^2x dx, so v = e^2x / 2

The above answers are wrong because exponents come first by default.

Integrate this expression using the power rule:
∫ x℮²x dx = ℮² ∫ x² dx
∫ x℮²x dx = ℮²x³ / 3 + C

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