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

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

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

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

\frac{ln ^{3} ( 2 )}{3}

Decimal Notation

0.11100 \dots

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{l n (2)}

= [\frac{u ^{3}}{3}]_{0}^{l n (2)}

Compute the boundaries:

\frac{ln ^{3} ( 2 )}{3}

= \frac{ln ^{3} ( 2 )}{3}

\int_{0}^{\infty} u (t) d t

x \to \infty lim (x \cdot 1)

3^{e^{x}}

\int t e^{- s t} d t

\frac{17}{4} - \frac{1}{x}, x, \frac{1}{4}, 4

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