What is the integral of (y/x) ?

The integral of (y/x) is yln|x|+C

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integral of (y/x)

\int (\frac{y}{x}) d x

y ln ∣ x ∣ + C

Solution steps

\int \frac{y}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= y \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y ln ∣ x ∣

Add a constant to the solution

= y ln ∣ x ∣ + C