What is the integral of (4x)/(3x^2) ?

The integral of (4x)/(3x^2) is 4/3 ln|x|+C

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integral of (4x)/(3x^2)

\int \frac{4 x}{3 x ^{2}} d x

\frac{4}{3} ln ∣ x ∣ + C

Solution steps

\int \frac{4 x}{3 x ^{2}} 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{x}{x ^{2}} d x

Cancel the common factor:

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

f (x) = \frac{x}{x + 7}

\int in (x + x^{2} + 1) d x

\frac{\partial}{\partial y} (x e^{y - 1})

\frac{d x}{d t} = 1.5 - \frac{2 x}{100 + t}

\int x (x - 6)^{2} d x

What is the integral of (4x)/(3x^2) ?
The integral of (4x)/(3x^2) is 4/3 ln|x|+C