Calculus Examples

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

Step 1

Split the single integral into multiple integrals.

$\int - \frac{2}{5} x d x + \int - 5 d x$

Step 2

Since $- \frac{2}{5}$ is constant with respect to $x$ , move $- \frac{2}{5}$ out of the integral.

$- \frac{2}{5} \int x d x + \int - 5 d x$

Step 3

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

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

Step 4

Apply the constant rule.

$- \frac{2}{5} (\frac{1}{2} x^{2} + C) - 5 x + C$

Step 5

Simplify.

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Step 5.1

Simplify.

$- \frac{2}{5} \cdot \frac{1}{2} x^{2} - 5 x + C$

Step 5.2

Simplify.

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Step 5.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{5}$ .

$- \frac{2}{2 \cdot 5} x^{2} - 5 x + C$

Step 5.2.2

Multiply $2$ by $5$ .

$- \frac{2}{10} x^{2} - 5 x + C$

Step 5.2.3

Cancel the common factor of $2$ and $10$ .

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Step 5.2.3.1

Factor $2$ out of $2$ .

$- \frac{2 (1)}{10} x^{2} - 5 x + C$

Step 5.2.3.2

Cancel the common factors.

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Step 5.2.3.2.1

Factor $2$ out of $10$ .

$- \frac{2 \cdot 1}{2 \cdot 5} x^{2} - 5 x + C$

Step 5.2.3.2.2

Cancel the common factor.

$- \frac{2 \cdot 1}{2 \cdot 5} x^{2} - 5 x + C$

Step 5.2.3.2.3

Rewrite the expression.

$- \frac{1}{5} x^{2} - 5 x + C$

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