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

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

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

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

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

Decimal

0.38472 \dots

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

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\int_{0}^{1} 2 π x (1 - x^{2}) d x

\int_{1}^{2} \frac{x}{x ^{2} + 2} d x

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