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

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

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integral of 1/(xln(4x))

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

ln ∣ ln (4 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 4 x )} 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 (4 x) ∣

Add a constant to the solution

= ln ∣ ln (4 x) ∣ + C

y = (\frac{4 x ^{2} - 5}{2 - x})^{3}

y^{^{'}} - \frac{2}{x} y = \frac{y ^{3}}{x ^{2}}, y (1) = 1

\frac{d}{d s} (\frac{1}{s ^{2} - 1})

\int \frac{csc ( θ )}{csc ( θ ) - sin ( θ )} d θ

\int 5 e^{- 2 t} sin (t) d t

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