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

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

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integral of 1/(xln(5x))

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

ln ∣ ln (5 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 5 x )} 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 (5 x) ∣

Add a constant to the solution

= ln ∣ ln (5 x) ∣ + C

\int (x^{3} - a^{3})^{5} d x

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\int (\frac{x}{3} + \frac{8}{x}) d x

\int \frac{5 x}{x ^{2} - 25} d x

\int (e π cos (t) + \frac{5}{e + e t ^{2}}) d t

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