(1 point)
Find the most general antiderivative of .
Note: Any arbitrary constants used must be an upper-case " C ".

Ask by Mathis Hammond. in the United States

Mar 30,2025

Question

(1 point) Find the most general antiderivative of $$ f(x)=2-1 x^{3}+3 x^{5}+4 x^{7} $$. Note: Any arbitrary constants used must be an upper-case " C ". $$ F(x)=\square $$

UpStudy AI · Accepted Answer

We integrate term by term:

1. For $$ 2 $$:  
   $$
   \int 2 \, dx = 2x
   $$

2. For $$-x^{3}$$:  
   $$
   \int (-x^{3}) \, dx = -\frac{x^4}{4}
   $$

3. For $$3x^{5}$$:  
   $$
   \int 3x^{5} \, dx = \frac{3x^6}{6} = \frac{x^6}{2}
   $$

4. For $$4x^{7}$$:  
   $$
   \int 4x^{7} \, dx = \frac{4x^8}{8} = \frac{x^8}{2}
   $$

Putting it all together and including the constant of integration, we have:
$$
F(x)=2x-\frac{x^4}{4}+\frac{x^6}{2}+\frac{x^8}{2}+ C
$$
$$ F(x) = 2x - \frac{x^4}{4} + \frac{x^6}{2} + \frac{x^8}{2} + C $$

(1 point)
Find the most general antiderivative of .
Note: Any arbitrary constants used must be an upper-case " C ".

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(1 point) Find the most general antiderivative of . Note: Any arbitrary constants used must be an upper-case " C ".