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

Simplify

= (- \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 ∣

Simplify

= - \frac{4}{3} ln ∣ x ∣

Add a constant to the solution

= - \frac{4}{3} ln ∣ x ∣ + C