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

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

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integral of 1/((xln(x)))

integral

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

ln ∣ ln (x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 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

\frac{2 sin ( x )}{cos ^{2} ( x )}

\frac{1}{x \cdot e ^{- x}}

(2 x + 5)^{5}

\frac{x}{( x ^{2} + 3 )}

\frac{1}{x ( 1 + x ) ^{\frac{1}{2}}}

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