Calculus Examples

$x^{- \frac{2}{3}}$

Step 1

Write $x^{- \frac{2}{3}}$ as a function.

$f (x) = x^{- \frac{2}{3}}$

Step 2

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int x^{- \frac{2}{3}} d x$

Step 4

By the Power Rule, the integral of $x^{- \frac{2}{3}}$ with respect to $x$ is $3 x^{\frac{1}{3}}$ .

$3 x^{\frac{1}{3}} + C$

Step 5

The answer is the antiderivative of the function $f (x) = x^{- \frac{2}{3}}$ .

$F (x) =$ $3 x^{\frac{1}{3}} + C$