What is the integral of 1/(12y) ?

The integral of 1/(12y) is 1/12 ln|y|+C

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integral of 1/(12y)

\int \frac{1}{12 y} d y

\frac{1}{12} ln ∣ y ∣ + C

Solution steps

\int \frac{1}{12 y} d y

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= \frac{1}{12} ln ∣ y ∣

Add a constant to the solution

= \frac{1}{12} ln ∣ y ∣ + C

\frac{\partial}{\partial y} (\frac{y - t}{5 y + 2 t})

t - π

\int \frac{x ^{2}}{( x ^{2} + 1 ) ^{2}} d x

\frac{d}{d x} (ln (x^{2} - 4))

\frac{d}{d t} (e^{5 t s i n (2 t)})