What is the integral of (a-b)/(bx) ?

The integral of (a-b)/(bx) is (a-b)/b ln|x|+C

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integral of (a-b)/(bx)

\int \frac{a - b}{b x} d x

\frac{a - b}{b} ln ∣ x ∣ + C

Solution steps

\int \frac{a - b}{b x} d x

Take the constant out:

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

= \frac{a - b}{b} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{a - b}{b} ln ∣ x ∣

Add a constant to the solution

= \frac{a - b}{b} ln ∣ x ∣ + C

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What is the integral of (a-b)/(bx) ?
The integral of (a-b)/(bx) is (a-b)/b ln|x|+C