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

The integral from 1 to infinity of (ln(x))/x is diverges

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integral from 1 to infinity of (ln(x))/x

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

diverges

Solution steps

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

Compute the indefinite integral:

\int \frac{ln ( x )}{x} d x = \frac{ln ^{2} ( x )}{2} + C

Compute the boundaries:

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

diverges

= diverges

\frac{d}{d x} (x^{4} - \frac{1}{x})

x \to 4 lim (x^{2} - 4 x + 1)

f (x) = 3 x - 5

\int \frac{16 x ^{2}}{( x - 9 ) ( x + 3 ) ^{2}} d x

\frac{d}{d x} ((5 x - 4) (2 x^{3} - x^{2} + 1))

What is the integral from 1 to infinity of (ln(x))/x ?
The integral from 1 to infinity of (ln(x))/x is diverges