What is the integral from 1 to 3 of 1/(x(ln(x))^2) ?

The integral from 1 to 3 of 1/(x(ln(x))^2) is diverges

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integral from 1 to 3 of 1/(x(ln(x))^2)

\int_{1}^{3} \frac{1}{x ( ln ( x ) ) ^{2}} d x

diverges

Solution steps

\int_{1}^{3} \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

: \int_{0}^{l n (3)} \frac{1}{u ^{2}} d u

= \int_{0}^{l n (3)} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{0}^{l n (3)}

= [- \frac{1}{u}]_{0}^{l n (3)}

Compute the boundaries:

diverges

= diverges

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What is the integral from 1 to 3 of 1/(x(ln(x))^2) ?
The integral from 1 to 3 of 1/(x(ln(x))^2) is diverges