## Final Answer

## Step-by-step Solution

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We can solve the integral $\int xe^xdx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

Learn how to solve definite integrals problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve definite integrals problems step by step online. Integrate the function xe^x from 0 to 2. We can solve the integral \int xe^xdx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.