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Compute an integral of (5x^4 – 4x^3)

Compute:

    \[ \int_{-1}^1 (5x^4 - 4x^3) \, dx. \]


Using the formula for the integral of polynomials, we compute:

    \[ \int_{-1}^1 (5x^4 - 4x^3) \, dx = \left. \left(5 \left(\frac{x^5}{5}\right) - 4 \left( \frac{x^4}{4} \right) \right) \right|_{-1}^1 = (1 - 1) - (-1 - 1) = 2. \]

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