Calculus Examples

$\frac{1}{z^{2}}$

Step 1

Apply basic rules of exponents.

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Step 1.1

Move $z^{2}$ out of the denominator by raising it to the $- 1$ power.

$\int {(z^{2})}^{- 1} d z$

Step 1.2

Multiply the exponents in ${(z^{2})}^{- 1}$ .

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Step 1.2.1

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

$\int z^{2 \cdot - 1} d z$

Step 1.2.2

Multiply $2$ by $- 1$ .

$\int z^{- 2} d z$

Step 2

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

$- z^{- 1} + C$

Step 3

Rewrite $- z^{- 1} + C$ as $- \frac{1}{z} + C$ .

$- \frac{1}{z} + C$