Find the Antiderivative (dy)/(y^2)

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

Write $\frac{d y}{y^{2}}$ as a function.

$f (d) = \frac{d y}{y^{2}}$

The function $F (d)$ can be found by finding the indefinite integral of the derivative $f (d)$ .

$F (d) = \int f (d) d \cdot d$

Set up the integral to solve.

$F (d) = \int \frac{d y}{y^{2}} d \cdot d$

Cancel the common factor of $y$ and $y^{2}$ .

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Factor $y$ out of $d y$ .

$\int \frac{y d}{y^{2}} d \cdot d$

Cancel the common factors.

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Factor $y$ out of $y^{2}$ .

$\int \frac{y d}{y \cdot y} d \cdot d$

Cancel the common factor.

$\int \frac{y d}{y \cdot y} d \cdot d$

Rewrite the expression.

$\int \frac{d}{y} d \cdot d$

Since $\frac{1}{y}$ is constant with respect to $d$ , move $\frac{1}{y}$ out of the integral.

$\frac{1}{y} \int d d \cdot d$

By the Power Rule, the integral of $d$ with respect to $d$ is $\frac{1}{2} d^{2}$ .

$\frac{1}{y} (\frac{1}{2} d^{2} + C)$

Simplify the answer.

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Simplify.

$\frac{1}{y} (\frac{1}{2} d^{2}) + C$

Simplify.

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Combine $\frac{1}{2}$ and $d^{2}$ .

$\frac{1}{y} \cdot \frac{d^{2}}{2} + C$

Multiply $\frac{1}{y}$ and $\frac{d^{2}}{2}$ .

$\frac{d^{2}}{y \cdot 2} + C$

Move $2$ to the left of $y$ .

$\frac{d^{2}}{2 y} + C$

The answer is the antiderivative of the function $f (d) = \frac{d y}{y^{2}}$ .

$F (d) =$ $\frac{d^{2}}{2 y} + C$

Find the Antiderivative (dy)/(y^2)

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