Calculus Examples

$\int - \frac{14 x^{\frac{5}{2}}}{2} d x$

Step 1

Simplify.

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Step 1.1

Factor $2$ out of $14 x^{\frac{5}{2}}$ .

$\int - \frac{2 (7 x^{\frac{5}{2}})}{2} d x$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\int - \frac{2 (7 x^{\frac{5}{2}})}{2 (1)} d x$

Step 1.2.2

Cancel the common factor.

$\int - \frac{2 (7 x^{\frac{5}{2}})}{2 \cdot 1} d x$

Step 1.2.3

Rewrite the expression.

$\int - \frac{7 x^{\frac{5}{2}}}{1} d x$

Step 1.2.4

Divide $7 x^{\frac{5}{2}}$ by $1$ .

$\int - (7 x^{\frac{5}{2}}) d x$

Step 1.3

Multiply $7$ by $- 1$ .

$\int - 7 x^{\frac{5}{2}} d x$

Step 2

Since $- 7$ is constant with respect to $x$ , move $- 7$ out of the integral.

$- 7 \int x^{\frac{5}{2}} d x$

Step 3

By the Power Rule, the integral of $x^{\frac{5}{2}}$ with respect to $x$ is $\frac{2}{7} x^{\frac{7}{2}}$ .

$- 7 (\frac{2}{7} x^{\frac{7}{2}} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $- 7 (\frac{2}{7} x^{\frac{7}{2}} + C)$ as $- 7 (\frac{2}{7}) x^{\frac{7}{2}} + C$ .

$- 7 (\frac{2}{7}) x^{\frac{7}{2}} + C$

Step 4.2

Simplify.

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Step 4.2.1

Combine $- 7$ and $\frac{2}{7}$ .

$\frac{- 7 \cdot 2}{7} x^{\frac{7}{2}} + C$

Step 4.2.2

Multiply $- 7$ by $2$ .

$\frac{- 14}{7} x^{\frac{7}{2}} + C$

Step 4.2.3

Cancel the common factor of $- 14$ and $7$ .

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Step 4.2.3.1

Factor $7$ out of $- 14$ .

$\frac{7 \cdot - 2}{7} x^{\frac{7}{2}} + C$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $7$ out of $7$ .

$\frac{7 \cdot - 2}{7 (1)} x^{\frac{7}{2}} + C$

Step 4.2.3.2.2

Cancel the common factor.

$\frac{7 \cdot - 2}{7 \cdot 1} x^{\frac{7}{2}} + C$

Step 4.2.3.2.3

Rewrite the expression.

$\frac{- 2}{1} x^{\frac{7}{2}} + C$

Step 4.2.3.2.4

Divide $- 2$ by $1$ .

$- 2 x^{\frac{7}{2}} + C$