What is the integral from 0 to 1 of 1/(xln(x)) ?

The integral from 0 to 1 of 1/(xln(x)) is diverges

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integral from 0 to 1 of 1/(xln(x))

\int_{0}^{1} \frac{1}{x ln ( x )} d x

diverges

Solution steps

\int_{0}^{1} \frac{1}{x ln ( x )} d x

Apply Integration By Parts

: [\frac{1}{ln ( x )} - \int - \frac{ln ( x ) + 1}{x ln ^{2} ( x )} d x]_{0}^{1}

= [\frac{1}{ln ( x )} - \int - \frac{ln ( x ) + 1}{x ln ^{2} ( x )} d x]_{0}^{1}

\int - \frac{ln ( x ) + 1}{x ln ^{2} ( x )} d x = - ln ∣ ln (x) ∣ + \frac{1}{ln ( x )}

= [\frac{1}{ln ( x )} - (- ln ∣ ln (x) ∣ + \frac{1}{ln ( x )})]_{0}^{1}

Simplify

= [ln ∣ ln (x) ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

y = e^{3 e^{x}}

f (x) = arctan (cos (x))

\frac{d}{d x} (4 x^{6} - 3 x^{5} - 10 x^{2} + 5 x + 16)

x \to 3 lim (6)

(1 + e^{x}) y y^{^{'}} = e^{x}

What is the integral from 0 to 1 of 1/(xln(x)) ?
The integral from 0 to 1 of 1/(xln(x)) is diverges