Question

Find the most general antiderivative for the function

Answer 1

Integrate.

Answer 2

\[f(x)=\frac{ 5 }{ \sqrt[3]{x}}-8\sqrt[3]{x^2}\]

Answer 3

please help I'm lost

Answer 4

hold on

Answer 5

rewrite them in index form

\[f(x) = 5x^{-\frac{1}{3}} - 8x^{\frac{2}{3}}\]

this should make it easier to find the antiderivative.

Answer 6

First factor out the constants.

\[5\int\limits_{?}^{?} 1 / \sqrt[3]{x}dx - 8\int\limits_{?}^{?}x^(2/3)dx\]

Answer 7

Second part should be x^(2/3)

Answer 8

Follow so far?

Answer 9

yes

Answer 10

what should i do now

Answer 11

Let's do the easy part first:
the integral of x^(2/3) is
3x^(5/3) / 5 (Don't forget about the constant; we'll multiply by that in a second)

You should get
\[- \frac{ 24x{^{5/3}} }{ 5 }\]

Follow so far?

Answer 12

ok thanks so much I think that i got the right answer now

Answer 13

I got 7.5x^2/3-4.8x^5/3

Answer 14

Bingo, congrats!