What is the integral of (1/(3x)) ?

The integral of (1/(3x)) is 1/3 ln|x|+C

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integral of (1/(3x))

\int (\frac{1}{3 x}) d x

\frac{1}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{1}{3 x} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ x ∣ + C

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

\int 10 x^{4} d x

y = 25 - x^{2}, (0, 5)

(t^{2} + 9) e^{t}

\frac{- 4 e ^{(- s)}}{( s ^{2} - 4 s + 3 )}