Calculus Examples

$\int (3 x^{4} - 4 + x^{- 2}) d x$

Step 1

Remove parentheses.

$\int 3 x^{4} - 4 + x^{- 2} d x$

Step 2

Split the single integral into multiple integrals.

$\int 3 x^{4} d x + \int - 4 d x + \int x^{- 2} d x$

Step 3

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

$3 \int x^{4} d x + \int - 4 d x + \int x^{- 2} d x$

Step 4

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

$3 (\frac{1}{5} x^{5} + C) + \int - 4 d x + \int x^{- 2} d x$

Step 5

Apply the constant rule.

$3 (\frac{1}{5} x^{5} + C) - 4 x + C + \int x^{- 2} d x$

Step 6

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

$3 (\frac{x^{5}}{5} + C) - 4 x + C + \int x^{- 2} d x$

Step 7

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

$3 (\frac{x^{5}}{5} + C) - 4 x + C - x^{- 1} + C$

Step 8

Simplify.

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Step 8.1

Simplify.

$\frac{3 x^{5}}{5} - 4 x - x^{- 1} + C$

Step 8.2

Reorder terms.

$\frac{3}{5} x^{5} - 4 x - x^{- 1} + C$