Calculus Examples

Evaluate $\int 4 x^{- 5} d x$

Step 1

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

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

Step 2

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

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

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Simplify.

Tap for more steps...

Step 3.1.1

Combine $x^{- 4}$ and $\frac{1}{4}$ .

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

Step 3.1.2

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3.2

Simplify.

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

Step 3.3

Simplify.

Tap for more steps...

Step 3.3.1

Multiply $- 1$ by $4$ .

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

Step 3.3.2

Combine $- 4$ and $\frac{1}{4 x^{4}}$ .

$\frac{- 4}{4 x^{4}} + C$

Step 3.3.3

Cancel the common factor of $- 4$ and $4$ .

Tap for more steps...

Step 3.3.3.1

Factor $4$ out of $- 4$ .

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

Step 3.3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.3.2.1

Factor $4$ out of $4 x^{4}$ .

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

Step 3.3.3.2.2

Cancel the common factor.

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

Step 3.3.3.2.3

Rewrite the expression.

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

Step 3.3.4

Move the negative in front of the fraction.

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