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

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

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integral of 1/(ln(x)x)

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

ln ∣ ln (x) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = ln (x)

= ln ∣ ln (x) ∣

Add a constant to the solution

= ln ∣ ln (x) ∣ + C

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

f (x) = (1 n (x^{3}))

x \to 19 lim (\frac{x - 19}{x ^{2} - 361})

\int e^{x} 31 + e^{x} d x

\frac{d y}{d x} = e^{2 x} - 3 y, y (0) = 2