What is the integral of (23)/(13-4x) ?

The integral of (23)/(13-4x) is -23/4 ln|13-4x|+C

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integral of (23)/(13-4x)

\int \frac{23}{13 - 4 x} d x

- \frac{23}{4} ln ∣ 13 - 4 x ∣ + C

Solution steps

\int \frac{23}{13 - 4 x} d x

Take the constant out:

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

= 23 \cdot \int \frac{1}{13 - 4 x} d x

Apply u-substitution

: \int - \frac{1}{4 u} d u

= 23 \cdot \int - \frac{1}{4 u} d u

Take the constant out:

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

= 23 (- \frac{1}{4} \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 23 (- \frac{1}{4} ln ∣ u ∣)

Substitute back

u = 13 - 4 x

= 23 (- \frac{1}{4} ln ∣ 13 - 4 x ∣)

Simplify

23 (- \frac{1}{4} ln ∣ 13 - 4 x ∣) : - \frac{23}{4} ln ∣ 13 - 4 x ∣

= - \frac{23}{4} ln ∣ 13 - 4 x ∣

Add a constant to the solution

= - \frac{23}{4} ln ∣ 13 - 4 x ∣ + C

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What is the integral of (23)/(13-4x) ?
The integral of (23)/(13-4x) is -23/4 ln|13-4x|+C