Question

exercises 4.10 antiderivatives
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consider the function f(x) = 2x⁸ + 9x⁷ − 5x³ − 1.
find the antiderivative such that f(x) = f(x).
you do not need to enter +c as it is already there after the answer box.
(2x⁹)/9 + 9x⁸ − (5x⁴)/4 − x × +c
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Explanation:

Step1: Integrate each term separately

Use the power rule for integration \(\int x^n dx=\frac{x^{n + 1}}{n+1}+C\) (\(n
eq - 1\)).
For the term \(2x^{8}\): \(\int2x^{8}dx=2\times\frac{x^{8 + 1}}{8+1}=\frac{2x^{9}}{9}\).
For the term \(9x^{7}\): \(\int9x^{7}dx=9\times\frac{x^{7+1}}{7 + 1}=\frac{9x^{8}}{8}\).
For the term \(-5x^{3}\): \(\int-5x^{3}dx=-5\times\frac{x^{3+1}}{3+1}=-\frac{5x^{4}}{4}\).
For the term \(-1\): \(\int-1dx=-x\).

Answer:

\(\frac{2x^{9}}{9}+\frac{9x^{8}}{8}-\frac{5x^{4}}{4}-x\)