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Evaluate: inte^x((x-4))/((x-2)^3)\ dx...

Evaluate: `inte^x((x-4))/((x-2)^3)\ dx`

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To evaluate the integral \( I = \int e^x \frac{x-4}{(x-2)^3} \, dx \), we will express the integrand in the form \( e^x (f(x) + f'(x)) \). ### Step 1: Identify \( f(x) \) We want to express \( \frac{x-4}{(x-2)^3} \) in the form \( f(x) + f'(x) \). Let's consider: \[ f(x) = \frac{1}{(x-2)^2} \] Then, we need to find \( f'(x) \). ...
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