Calculus Examples

$\int (- 6 - 4 x^{5} + x^{4}) d x$

Step 1

Remove parentheses.

$\int - 6 - 4 x^{5} + x^{4} d x$

Step 2

Split the single integral into multiple integrals.

$\int - 6 d x + \int - 4 x^{5} d x + \int x^{4} d x$

Step 3

Apply the constant rule.

$- 6 x + C + \int - 4 x^{5} d x + \int x^{4} d x$

Step 4

Since $- 4$ is constant with respect to $x$ , move $- 4$ out of the integral.

$- 6 x + C - 4 \int x^{5} d x + \int x^{4} d x$

Step 5

By the Power Rule, the integral of $x^{5}$ with respect to $x$ is $\frac{1}{6} x^{6}$ .

$- 6 x + C - 4 (\frac{1}{6} x^{6} + C) + \int x^{4} d x$

Step 6

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

$- 6 x + C - 4 (\frac{1}{6} x^{6} + C) + \frac{1}{5} x^{5} + C$

Step 7

Simplify.

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Step 7.1

Combine $\frac{1}{6}$ and $x^{6}$ .

$- 6 x + C - 4 (\frac{x^{6}}{6} + C) + \frac{1}{5} x^{5} + C$

Step 7.2

Simplify.

$- 6 x - \frac{2 x^{6}}{3} + \frac{1}{5} x^{5} + C$

Step 8

Reorder terms.

$- 6 x - \frac{2}{3} x^{6} + \frac{1}{5} x^{5} + C$