What is the integral of (5z^2)/y ?

The integral of (5z^2)/y is 5z^2ln|y|+C

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integral of (5z^2)/y

\int \frac{5 z ^{2}}{y} d y

5 z^{2} ln ∣ y ∣ + C

Solution steps

\int \frac{5 z ^{2}}{y} d y

Take the constant out:

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

= 5 z^{2} \cdot \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= 5 z^{2} ln ∣ y ∣

Add a constant to the solution

= 5 z^{2} ln ∣ y ∣ + C

lo g_{5} (x^{4})

\frac{\partial}{\partial y} (x - 1)

\frac{\partial}{\partial x} ((2 x - 3 y)^{3})

x \to 4 lim (\frac{1}{x - 2})

f (x) = \frac{4}{x} a = \frac{1}{16}