Calculus Examples

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

Step 1

Apply basic rules of exponents.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Multiply $2$ by $- 1$ .

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

Step 2

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

$- y^{- 1} + C$

Step 3

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

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