What is the integral of 1/(x(ln(2x))) ?

The integral of 1/(x(ln(2x))) is ln|ln(2x)|+C

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integral of 1/(x(ln(2x)))

\int \frac{1}{x ( ln ( 2 x ) )} d x

ln ∣ ln (2 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 2 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 (2 x) ∣

Add a constant to the solution

= ln ∣ ln (2 x) ∣ + C

(40 cos (20 t - \frac{π}{2}))^{^{'}}

\int t e^{- 7 t} d t

x \to 2 lim (\frac{2 x}{x ^{2} - 4})

\int \frac{1}{4 + 3 x} d x

\frac{d y}{d x} = e^{y + 2 x}

What is the integral of 1/(x(ln(2x))) ?
The integral of 1/(x(ln(2x))) is ln|ln(2x)|+C