Calculus Examples

$\int 5 x - 5 d x$

Step 1

Split the single integral into multiple integrals.

$\int 5 x d x + \int - 5 d x$

Step 2

Since $5$ is constant with respect to $x$ , move $5$ out of the integral.

$5 \int x d x + \int - 5 d x$

Step 3

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

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

Step 4

Apply the constant rule.

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

Step 5

Simplify.

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Step 5.1

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

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

Step 5.2

Simplify.

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

Step 5.3

Reorder terms.

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

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