What is the integral of 1/((x-4)ln(x-4)) ?

The integral of 1/((x-4)ln(x-4)) is ln|ln(x-4)|+C

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integral of 1/((x-4)ln(x-4))

\int \frac{1}{( x - 4 ) ln ( x - 4 )} d x

ln ∣ ln (x - 4) ∣ + C

Solution steps

\int \frac{1}{( x - 4 ) ln ( x - 4 )} d x

Apply u-substitution

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (x - 4) ∣

Add a constant to the solution

= ln ∣ ln (x - 4) ∣ + C

What is the integral of 1/((x-4)ln(x-4)) ?
The integral of 1/((x-4)ln(x-4)) is ln|ln(x-4)|+C