What is the integral of 4/(3x) ?

The integral of 4/(3x) is 4/3 ln|x|+C

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integral of 4/(3x)

\int \frac{4}{3 x} d x

\frac{4}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{4}{3 x} d x

Take the constant out:

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

= \frac{4}{3} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{4}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{4}{3} ln ∣ x ∣ + C

y = ln (x^{2} + 3)

n = 1 \sum \infty \frac{n !}{10 0 ^{n}}

\frac{d}{d x} (sin (5 x) + tan (3 x))

x^{^{''}} + 2 x^{^{'}} + 10 = e^{- t}, x (0) = 0, x^{^{'}} (0) = 0