What is the integral of-1/(2/x y) ?

The integral of-1/(2/x y) is -x/2 ln|y|+C

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integral of-1/(2/x y)

\int - \frac{1}{\frac{2}{x} y} d y

- \frac{x}{2} ln ∣ y ∣ + C

Solution steps

\int - \frac{1}{\frac{2}{x} y} d y

Take the constant out:

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

= - \frac{1}{\frac{2}{x}} \cdot \int \frac{1}{y} d y

Simplify

= - \frac{x}{2} \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= - \frac{x}{2} ln ∣ y ∣

Add a constant to the solution

= - \frac{x}{2} ln ∣ y ∣ + C

sin (tan (5 x))

\frac{d}{d x} (- 2 (e^{- x^{2}} - 2 e^{- x^{2}} x^{2}))

\frac{\partial}{\partial x} (x y + x z - 2 yz)

f (x) = x^{2}

\frac{\partial}{\partial x} (ln (x))