Calculus Examples

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

Step 1

Write $\frac{1}{y} d y$ as a function.

$f (y) = \frac{1}{y} d y$

Step 2

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

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

Step 3

Set up the integral to solve.

$F (y) = \int \frac{1}{y} \cdot (d y) d y$

Step 4

Simplify.

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Step 4.1

Combine $d$ and $\frac{1}{y}$ .

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

Step 4.2

Combine $\frac{d}{y}$ and $y$ .

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

Step 4.3

Cancel the common factor of $y$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Divide $d$ by $1$ .

$\int d d y$

Step 5

Apply the constant rule.

$d y + C$

Step 6

The answer is the antiderivative of the function $f (y) = \frac{1}{y} \cdot (d y)$ .

$F (y) =$ $d y + C$