Calculus Examples

${(\sqrt{- 12})}^{3}$

Step 1

Simplify.

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Step 1.1

Rewrite ${(\sqrt{- 12})}^{3}$ as $\sqrt{{(- 12)}^{3}}$ .

$\int \sqrt{{(- 12)}^{3}} d x$

Step 1.2

Raise $- 12$ to the power of $3$ .

$\int \sqrt{- 1728} d x$

Step 2

Apply the constant rule.

$\sqrt{- 1728} x + C$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $\sqrt{- 1728} x + C$ as $i \cdot \sqrt{1728} x + C$ .

$i \cdot \sqrt{1728} x + C$

Step 3.2

Simplify.

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Step 3.2.1

Rewrite $1728$ as $24^{2} \cdot 3$ .

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Step 3.2.1.1

Factor $576$ out of $1728$ .

$i \cdot \sqrt{576 (3)} x + C$

Step 3.2.1.2

Rewrite $576$ as $24^{2}$ .

$i \cdot \sqrt{24^{2} \cdot 3} x + C$

Step 3.2.2

Pull terms out from under the radical.

$i \cdot (24 \sqrt{3}) x + C$

Step 3.2.3

Move $24$ to the left of $i$ .

$24 i \sqrt{3} x + C$