What is the integral of-(12)/y ?

The integral of-(12)/y is -12ln|y|+C

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integral of-(12)/y

\int - \frac{12}{y} d y

- 12 ln ∣ y ∣ + C

Solution steps

\int - \frac{12}{y} d y

Take the constant out:

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

= - 12 \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= - 12 ln ∣ y ∣

Add a constant to the solution

= - 12 ln ∣ y ∣ + C

\frac{\partial}{\partial x} (- 3 x y sin (z))

\frac{d}{d x} (\frac{1}{9} ln (- ln (x)) + 5)

x \frac{d y}{d x} + 3 y = 2 x^{5}

\int \frac{3 x + 6}{x ^{2} + 2 x + 2} d x

\int_{0}^{4} x + 3 x d x