`f(x) = 8x^9 - 3x^6 + 12x^3` Find the most general antiderivative of the function. (Check your answer by differentiation.)

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Chapter 4, 4.9 - Problem 4 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the most antiderivative of the function, such that:

`int f(x) dx = F(x) + c`

`int (8x^9 - 3x^6 + 12x^3) dx = int8x^9 dx - int 3x^6dx+ int12x^3 dx`

`int (8x^9 - 3x^6 + 12x^3) dx = (8/10)x^10 - (3/7)x^7 + 3x^4 + c`

`int (8x^9 - 3x^6 + 12x^3) dx = (4/5)x^10 - (3/7)x^7 + 3x^4 + c`

Hence, evaluating the most antiderivative of the function yields `F(x) = (4/5)x^10 - (3/7)x^7 + 3x^4 + c.`

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