Calculus Examples

$\int (- 3 x^{4} - 6) d x$

Step 1

Remove parentheses.

$\int - 3 x^{4} - 6 d x$

Step 2

Split the single integral into multiple integrals.

$\int - 3 x^{4} d x + \int - 6 d x$

Step 3

Since $- 3$ is constant with respect to $x$ , move $- 3$ out of the integral.

$- 3 \int x^{4} d x + \int - 6 d x$

Step 4

By the Power Rule, the integral of $x^{4}$ with respect to $x$ is $\frac{1}{5} x^{5}$ .

$- 3 (\frac{1}{5} x^{5} + C) + \int - 6 d x$

Step 5

Apply the constant rule.

$- 3 (\frac{1}{5} x^{5} + C) - 6 x + C$

Step 6

Simplify.

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Step 6.1

Combine $\frac{1}{5}$ and $x^{5}$ .

$- 3 (\frac{x^{5}}{5} + C) - 6 x + C$

Step 6.2

Simplify.

$\frac{- 3 x^{5}}{5} - 6 x + C$

Step 6.3

Move the negative in front of the fraction.

$- \frac{3 x^{5}}{5} - 6 x + C$

Step 7

Reorder terms.

$- \frac{3}{5} x^{5} - 6 x + C$