What is the integral from 0 to 10 of (ln(x))/x ?

The integral from 0 to 10 of (ln(x))/x is diverges

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integral from 0 to 10 of (ln(x))/x

\int_{0}^{10} \frac{ln ( x )}{x} d x

diverges

Solution steps

\int_{0}^{10} \frac{ln ( x )}{x} d x

Apply Integration By Parts

: [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{10}

= [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{10}

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

= [ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{10}

Simplify

[ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{10} : [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{10}

= [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{10}

Compute the boundaries:

diverges

= diverges

\int_{- 2}^{2} (x^{2} + 2) d x

\int_{- 5}^{10} e^{- 0.05 x} d x

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\int_{0}^{l n (2 x)} sin (5 e^{t}) d t

\int_{0}^{1} 2 x (x^{2} + \frac{1}{2})^{2} d x

What is the integral from 0 to 10 of (ln(x))/x ?
The integral from 0 to 10 of (ln(x))/x is diverges