What is the integral of 1/(xlog_{x)(x)} ?

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

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integral of 1/(xlog_{x)(x)}

\int \frac{1}{x lo g _{x} ( x )} d x

ln ∣ x ∣ + C

Solution steps

\int \frac{1}{x lo g _{x} ( x )} d x

Simplify

\frac{1}{x lo g _{x} ( x )} : \frac{1}{x}

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

\frac{d y}{d x} = x^{2} + 1

\frac{d}{d x} (8 7 x^{2} + 5)

\int \frac{e ^{x}}{4 + e ^{2 x}} d x

\frac{d}{d x} (\frac{x}{x - 10})

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

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