Calculus Examples

$\frac{17}{2} \cdot ({(2)}^{2} arcsec (2)) - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3}))$

Step 1

Simplify.

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Step 1.1

Raise $2$ to the power of $2$ .

$\int \frac{17}{2} \cdot (4 arcsec (2)) - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.2

Combine $4$ and $\frac{17}{2}$ .

$\int \frac{4 \cdot 17}{2} \cdot arcsec (2) - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.3

Multiply $4$ by $17$ .

$\int \frac{68}{2} \cdot arcsec (2) - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.4

Combine $\frac{68}{2}$ and $arcsec (2)$ .

$\int \frac{68 arcsec (2)}{2} - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.5

Cancel the common factor of $68$ and $2$ .

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Step 1.5.1

Factor $2$ out of $68 arcsec (2)$ .

$\int \frac{2 (34 arcsec (2))}{2} - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $2$ .

$\int \frac{2 (34 arcsec (2))}{2 (1)} - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.5.2.2

Cancel the common factor.

$\int \frac{2 (34 arcsec (2))}{2 \cdot 1} - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.5.2.3

Rewrite the expression.

$\int \frac{34 arcsec (2)}{1} - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.5.2.4

Divide $34 arcsec (2)$ by $1$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot ({(2 \sqrt{3})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.6

Factor $2$ out of $2 \sqrt{3}$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot ({(2 (\sqrt{3}))}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.7

Apply the product rule to $2 (\sqrt{3})$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (2^{2} {\sqrt{3}}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.8

Raise $2$ to the power of $2$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 {\sqrt{3}}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.9

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 1.9.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 {(3^{\frac{1}{2}})}^{2} arcsec (2 \sqrt{3})) d x$

Step 1.9.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 \cdot 3^{\frac{1}{2} \cdot 2} arcsec (2 \sqrt{3})) d x$

Step 1.9.3

Combine $\frac{1}{2}$ and $2$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 \cdot 3^{\frac{2}{2}} arcsec (2 \sqrt{3})) d x$

Step 1.9.4

Cancel the common factor of $2$ .

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Step 1.9.4.1

Cancel the common factor.

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 \cdot 3^{\frac{2}{2}} arcsec (2 \sqrt{3})) d x$

Step 1.9.4.2

Rewrite the expression.

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 \cdot 3^{1} arcsec (2 \sqrt{3})) d x$

Step 1.9.5

Evaluate the exponent.

$\int 34 arcsec (2) - \frac{17}{2} \cdot (4 \cdot 3 arcsec (2 \sqrt{3})) d x$

Step 1.10

Multiply $4$ by $3$ .

$\int 34 arcsec (2) - \frac{17}{2} \cdot (12 arcsec (2 \sqrt{3})) d x$

Step 1.11

Multiply $12$ by $- 1$ .

$\int 34 arcsec (2) - 12 (\frac{17}{2}) \cdot arcsec (2 \sqrt{3}) d x$

Step 1.12

Combine $- 12$ and $\frac{17}{2}$ .

$\int 34 arcsec (2) + \frac{- 12 \cdot 17}{2} \cdot arcsec (2 \sqrt{3}) d x$

Step 1.13

Multiply $- 12$ by $17$ .

$\int 34 arcsec (2) + \frac{- 204}{2} \cdot arcsec (2 \sqrt{3}) d x$

Step 1.14

Combine $\frac{- 204}{2}$ and $arcsec (2 \sqrt{3})$ .

$\int 34 arcsec (2) + \frac{- 204 arcsec (2 \sqrt{3})}{2} d x$

Step 1.15

Cancel the common factor of $- 204$ and $2$ .

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Step 1.15.1

Factor $2$ out of $- 204 arcsec (2 \sqrt{3})$ .

$\int 34 arcsec (2) + \frac{2 (- 102 arcsec (2 \sqrt{3}))}{2} d x$

Step 1.15.2

Cancel the common factors.

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Step 1.15.2.1

Factor $2$ out of $2$ .

$\int 34 arcsec (2) + \frac{2 (- 102 arcsec (2 \sqrt{3}))}{2 (1)} d x$

Step 1.15.2.2

Cancel the common factor.

$\int 34 arcsec (2) + \frac{2 (- 102 arcsec (2 \sqrt{3}))}{2 \cdot 1} d x$

Step 1.15.2.3

Rewrite the expression.

$\int 34 arcsec (2) + \frac{- 102 arcsec (2 \sqrt{3})}{1} d x$

Step 1.15.2.4

Divide $- 102 arcsec (2 \sqrt{3})$ by $1$ .

$\int 34 arcsec (2) - 102 arcsec (2 \sqrt{3}) d x$

Step 2

Apply the constant rule.

$(34 arcsec (2) - 102 arcsec (2 \sqrt{3})) x + C$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $(34 arcsec (2) - 102 arcsec (2 \sqrt{3})) x + C$ as $(\frac{34 π}{3} - 130.35126261) x + C$ .

$(\frac{34 π}{3} - 130.35126261) x + C$

Step 3.2

Subtract $130.35126261$ from $\frac{34 π}{3}$ .

$- 94.74654587 x + C$