Calculus Examples

$\int \frac{1}{x^{12}} d x$

Step 1

Apply basic rules of exponents.

Tap for more steps...

Step 1.1

Move $x^{12}$ out of the denominator by raising it to the $- 1$ power.

$\int {(x^{12})}^{- 1} d x$

Step 1.2

Multiply the exponents in ${(x^{12})}^{- 1}$ .

Tap for more steps...

Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\int x^{12 \cdot - 1} d x$

Step 1.2.2

Multiply $12$ by $- 1$ .

$\int x^{- 12} d x$

Step 2

By the Power Rule, the integral of $x^{- 12}$ with respect to $x$ is $- \frac{1}{11} x^{- 11}$ .

$- \frac{1}{11} x^{- 11} + C$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite $- \frac{1}{11} x^{- 11} + C$ as $- \frac{1}{11} \cdot \frac{1}{x^{11}} + C$ .

$- \frac{1}{11} \cdot \frac{1}{x^{11}} + C$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Multiply $\frac{1}{x^{11}}$ by $\frac{1}{11}$ .

$- \frac{1}{x^{11} \cdot 11} + C$

Step 3.2.2

Move $11$ to the left of $x^{11}$ .

$- \frac{1}{11 x^{11}} + C$