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

The integral from 1 to e^2 of ((ln(x))^2)/x is 8/3

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

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

\frac{8}{3}

Decimal

2.66666 \dots

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{0}^{2}

Compute the boundaries:

\frac{8}{3}

= \frac{8}{3}

\int_{0}^{1} sin (π) x d x

\int_{0}^{9} x^{2} - 1 d x

\int_{1}^{x} tan (t) d t

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

\int_{0}^{\frac{π}{2}} sin^{8} (x) d x

What is the integral from 1 to e^2 of ((ln(x))^2)/x ?
The integral from 1 to e^2 of ((ln(x))^2)/x is 8/3