Question

consider the function $f(x) = 2x^8 + 4x^5 - 10x^2 - 5$. enter an antiderivative such that $f = f(x)$. do not enter $+c$ as part of your answer, as it is already there after the answer box. $f(x) = \boxed{} + c$ question help: \\( \boldsymbol{\text{message instructor}} \\) \\( \boldsymbol{\text{submit question}} \\) \\( \boldsymbol{\text{jump to answer}} \\)

Explanation:

Step1: Integrate each term

Use the power rule for integration \(\int x^n dx=\frac{x^{n + 1}}{n+1}\) (\(n
eq - 1\)).
For the term \(2x^{8}\): \(\int2x^{8}dx=2\times\frac{x^{8 + 1}}{8+1}=\frac{2x^{9}}{9}\).
For the term \(4x^{5}\): \(\int4x^{5}dx=4\times\frac{x^{5+1}}{5 + 1}=\frac{4x^{6}}{6}=\frac{2x^{6}}{3}\).
For the term \(-10x^{2}\): \(\int-10x^{2}dx=-10\times\frac{x^{2+1}}{2+1}=-\frac{10x^{3}}{3}\).
For the term \(-5\): \(\int-5dx=-5x\).

Step2: Combine the integrated terms

\(F(x)=\frac{2x^{9}}{9}+\frac{2x^{6}}{3}-\frac{10x^{3}}{3}-5x\).

Answer:

\(\frac{2x^{9}}{9}+\frac{2x^{6}}{3}-\frac{10x^{3}}{3}-5x\)