What is the integral of 2/(3x) ?

The integral of 2/(3x) is 2/3 ln|x|+C

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integral of 2/(3x)

\int \frac{2}{3 x} d x

\frac{2}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{2}{3 x} d x

Take the constant out:

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

= \frac{2}{3} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{2}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{2}{3} ln ∣ x ∣ + C

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 7

y^{^{''}} + \frac{3}{x} y^{^{'}} = 0

\frac{d y}{d x} = \frac{8 x}{5 y}

\int (x^{2} + 4)^{2} d x

x \to \infty lim (- 5 x^{3})