What is the integral from 1 to 4 of (sqrt(ln(x)))/x ?

The integral from 1 to 4 of (sqrt(ln(x)))/x is (4sqrt(2))/3 ln^{3/2}(2)

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integral from 1 to 4 of (sqrt(ln(x)))/x

\int_{1}^{4} \frac{ln ( x )}{x} d x

\frac{4 2}{3} ln^{\frac{3}{2}} (2)

Decimal

1.08815 \dots

Solution steps

\int_{1}^{4} \frac{ln ( x )}{x} d x

Apply u-substitution

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

Apply the Power Rule

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

Compute the boundaries:

\frac{4 2}{3} ln^{\frac{3}{2}} (2)

= \frac{4 2}{3} ln^{\frac{3}{2}} (2)

What is the integral from 1 to 4 of (sqrt(ln(x)))/x ?
The integral from 1 to 4 of (sqrt(ln(x)))/x is (4sqrt(2))/3 ln^{3/2}(2)