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Answer :
The antiderivative of the given function f(x) = 5x^8 + 8x^7 – 9x^2 – 9 is found by integrating each term separately. The result is F(x) = (5/9)x^9 + x^8 - 3x^3 - 9x + C, with C being the constant of integration.
The antiderivative is the reverse process of differentiation, meaning we are looking for a function whose derivative gives us the original function f(x). Given the function f(x) = 5x^8 + 8x^7 – 9x^2 – 9, we find the antiderivative by integrating each term seperately:
Integral of 5x^8 is (5/9)x^9
Integral of 8x^7 is x^8
Integral of -9x^2 is (-9/3)x^3
Integral of -9 is -9x
Summing these together, we get an antiderivative of the original function as F(x) = (5/9)x^9 + x^8 - 3x^3 - 9x + C, where C is the constant of integration, representing all possible vertical shifts of the antiderivative.
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