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

The integral from e to e^2 of (ln(x))^2(1/x) is 7/3

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

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

\frac{7}{3}

Decimal Notation

2.33333 \dots

Solution steps

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

Simplify

(ln (x))^{2} \frac{1}{x} : \frac{ln ^{2} ( x )}{x}

= \int_{e}^{e^{2}} \frac{ln ^{2} ( x )}{x} d x

Apply u-substitution

: \int_{1}^{2} u^{2} d u

= \int_{1}^{2} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{1}^{2}

= [\frac{u ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= \frac{7}{3}

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

\int_{- 3}^{- 1} x^{2} - 2 x d x

What is the integral from e to e^2 of (ln(x))^2(1/x) ?
The integral from e to e^2 of (ln(x))^2(1/x) is 7/3