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Evaluate: inte^x(x-1)/((x+1)^3)\ dx...

Evaluate: `inte^x(x-1)/((x+1)^3)\ dx`

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To evaluate the integral \( I = \int \frac{e^x (x - 1)}{(x + 1)^3} \, dx \), we can use the method of integration by recognizing a suitable function and its derivative. ### Step-by-Step Solution: 1. **Identify the structure of the integrand**: We want to express \( \frac{x - 1}{(x + 1)^3} \) in the form \( f(x) + f'(x) \). 2. **Assume a function**: ...
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