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To solve the integral 

\[
\int_{0}^{2} e^{2x} \cos(x - 2) \, dx
\]

we'll use integration techniques for functions of the form \( e^{ax} \cos(bx + c) \). This generally involves integration by parts or leveraging known integration formulas for such expressions.

The solution process will be carried out as follows:

1. **Rewrite the integral using known identities** if needed.
2. **Apply integration techniques** like integration by parts or look up a formula for integrating \( e^{ax} \cos(bx + c) \).
3. **Evaluate the result from 0 to 2**.

Let's calculate this and round it to two decimal places.

Compute \( \int_{0}^{2} e^{2x} \cos(x - 2) \, dx \) with two decimal places.

Learn how to compute the integral \( \int_{0}^{2} e^{2x} \cos(x - 2) \, dx \) with a step-by-step solution. This problem covers techniques like integration by parts and known integration formulas for exponential and trigonometric functions, suitable for undergraduate calculus students.

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