What is the integral of-5/(3x) ?

The integral of-5/(3x) is -5/3 ln|x|+C

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integral of-5/(3x)

\int - \frac{5}{3 x} d x

- \frac{5}{3} ln ∣ x ∣ + C

Solution steps

\int - \frac{5}{3 x} d x

Take the constant out:

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

= - \frac{5}{3} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - \frac{5}{3} ln ∣ x ∣

Add a constant to the solution

= - \frac{5}{3} ln ∣ x ∣ + C

\frac{( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 )}

\frac{\partial}{\partial x} (\frac{4 x - 3 t}{s + 2 x})

\frac{\partial}{\partial x} (x - cos (x))

y^{^{'}} = y x

x \to 0 lim (+ \frac{x ^{3} + 3}{x})