What is the integral from 1 to e^9 of ((ln(x))^2)/x ?

The integral from 1 to e^9 of ((ln(x))^2)/x is 243

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integral from 1 to e^9 of ((ln(x))^2)/x

\int_{1}^{e^{9}} \frac{( ln ( x ) ) ^{2}}{x} d x

243

Solution steps

\int_{1}^{e^{9}} \frac{( ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

: \int_{0}^{9} u^{2} d u

= \int_{0}^{9} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{9}

= [\frac{u ^{3}}{3}]_{0}^{9}

Compute the boundaries:

243

= 243

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What is the integral from 1 to e^9 of ((ln(x))^2)/x ?
The integral from 1 to e^9 of ((ln(x))^2)/x is 243