Calculus Examples

$\int (x^{- 2} - 6 + x^{5}) d x$

Step 1

Remove parentheses.

$\int x^{- 2} - 6 + x^{5} d x$

Step 2

Split the single integral into multiple integrals.

$\int x^{- 2} d x + \int - 6 d x + \int x^{5} d x$

Step 3

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

$- x^{- 1} + C + \int - 6 d x + \int x^{5} d x$

Step 4

Apply the constant rule.

$- x^{- 1} + C - 6 x + C + \int x^{5} d x$

Step 5

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

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

Step 6

Simplify.

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