What is the integral of 1/((x-5)ln(x-5)) ?

The integral of 1/((x-5)ln(x-5)) is ln|ln(x-5)|+C

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integral of 1/((x-5)ln(x-5))

\int \frac{1}{( x - 5 ) ln ( x - 5 )} d x

ln ∣ ln (x - 5) ∣ + C

Solution steps

\int \frac{1}{( x - 5 ) ln ( x - 5 )} d x

Apply u-substitution

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

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

Apply u-substitution

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

= \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 - 5) ∣

Add a constant to the solution

= ln ∣ ln (x - 5) ∣ + C

\int 7 e^{4 x} d x

\int_{2}^{\infty} e^{- 3 x} d x

(2, 5), (8, - 4)

\frac{d}{d t} (\frac{7}{t})

\frac{sin ( ln ( 4 ) x ^{2} )}{x}

What is the integral of 1/((x-5)ln(x-5)) ?
The integral of 1/((x-5)ln(x-5)) is ln|ln(x-5)|+C