Calculus Examples

$\int 9 x^{- \frac{4}{5}} d x$

Step 1

Since $9$ is constant with respect to $x$ , move $9$ out of the integral.

$9 \int x^{- \frac{4}{5}} d x$

Step 2

By the Power Rule, the integral of $x^{- \frac{4}{5}}$ with respect to $x$ is $5 x^{\frac{1}{5}}$ .

$9 (5 x^{\frac{1}{5}} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $9 (5 x^{\frac{1}{5}} + C)$ as $9 \cdot 5 x^{\frac{1}{5}} + C$ .

$9 \cdot 5 x^{\frac{1}{5}} + C$

Step 3.2

Multiply $9$ by $5$ .

$45 x^{\frac{1}{5}} + C$