What is the integral of (15)/(15x-3) ?

The integral of (15)/(15x-3) is ln|15x-3|+C

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integral of (15)/(15x-3)

\int \frac{15}{15 x - 3} d x

ln ∣ 15 x - 3 ∣ + C

Solution steps

\int \frac{15}{15 x - 3} d x

Take the constant out:

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

= 15 \cdot \int \frac{1}{15 x - 3} d x

Apply u-substitution

: \int \frac{1}{15 u} d u

= 15 \cdot \int \frac{1}{15 u} d u

Take the constant out:

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

= 15 \cdot \frac{1}{15} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 15 \cdot \frac{1}{15} ln ∣ u ∣

Substitute back

u = 15 x - 3

= 15 \cdot \frac{1}{15} ln ∣ 15 x - 3 ∣

Simplify

15 \cdot \frac{1}{15} ln ∣ 15 x - 3 ∣ : ln ∣ 15 x - 3 ∣

= ln ∣ 15 x - 3 ∣

Add a constant to the solution

= ln ∣ 15 x - 3 ∣ + C

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What is the integral of (15)/(15x-3) ?
The integral of (15)/(15x-3) is ln|15x-3|+C