Calculus Examples

$\int x^{3} - 5 x d x$

Step 1

Split the single integral into multiple integrals.

$\int x^{3} d x + \int - 5 x d x$

Step 2

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$\frac{1}{4} x^{4} + C + \int - 5 x d x$

Step 3

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

$\frac{1}{4} x^{4} + C - 5 \int x d x$

Step 4

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

$\frac{1}{4} x^{4} + C - 5 (\frac{1}{2} x^{2} + C)$

Step 5

Simplify.

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Step 5.1

Simplify.

$\frac{1}{4} x^{4} - 5 (\frac{1}{2}) x^{2} + C$

Step 5.2

Simplify.

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Step 5.2.1

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{1}{4} x^{4} + \frac{- 5}{2} x^{2} + C$

Step 5.2.2

Move the negative in front of the fraction.

$\frac{1}{4} x^{4} - \frac{5}{2} x^{2} + C$