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

\frac{\partial}{\partial y} (cos (x) + sin (y))

f (x) = 3 6 x + 8

\frac{d}{d x} (tan^{2} (sin (x)))

f (x) = x + 7

x = \frac{( y - 2 ) ^{2}}{3}, y = 8 - x