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30 November, 12:44

antiderivative of Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f (x) = 6 x 5 - 8x4 - 9x2.) f (x) = 6x5 - 8x4 - 9x2 the function.

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  1. 30 November, 14:43
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    x^6 - (8/5) x^5 - 3x^3 + C.

    Step-by-step explanation:

    f (x) = 6x^5 - 8x^4 - 9x^2.

    Using the general form antiderivative of Ax^m = Ax (m+1) / (m+1) + C:

    Antiderivative = 6 * x^ (5+1) / 6 - 8 * x^ (4+1) / 5 - 9 * x^ (2+1) / 3 + C

    = 6x^6/6 - 8x^5/5 - 9x^3/3 + C

    = x^6 - (8/5) x^5 - 3x^3 + C.

    Differentiating:

    f' (x) = 6x^ (6-1) - 8 x^ (5-4) - 9x^ (3-1) + 0

    f' (x) = 6x^5 - 8x^4 - 9x^2.
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