What is the integral of 1/(5y) ?

The integral of 1/(5y) is 1/5 ln|y|+C

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integral of 1/(5y)

\int \frac{1}{5 y} d y

\frac{1}{5} ln ∣ y ∣ + C

Solution steps

\int \frac{1}{5 y} d y

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= \frac{1}{5} ln ∣ y ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ y ∣ + C

y^{^{''}} + y = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 8

\frac{\partial}{\partial x} (3 x + 9 x^{17})

x \to 0 - lim (x^{3} cos (\frac{2}{x}))

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{3}})