What is the integral of-4/y ?

The integral of-4/y is -4ln|y|+C

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integral of-4/y

\int - \frac{4}{y} d y

- 4 ln ∣ y ∣ + C

Solution steps

\int - \frac{4}{y} d y

Take the constant out:

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

= - 4 \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= - 4 ln ∣ y ∣

Add a constant to the solution

= - 4 ln ∣ y ∣ + C

y = - 7 - 3 x

y^{^{'}} + \frac{1}{x} y = \frac{2}{3} x^{2} y^{2}

\int sec^{6} (x) d x

x \to π + lim (cot (x))

\frac{d ^{2}}{d x ^{2}} (5 x^{\frac{3}{2}})