What is the integral from 1 to 7 of (ln(x))/x ?

The integral from 1 to 7 of (ln(x))/x is (ln^2(7))/2

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integral from 1 to 7 of (ln(x))/x

\int_{1}^{7} \frac{ln ( x )}{x} d x

\frac{ln ^{2} ( 7 )}{2}

Decimal Notation

1.89328 \dots

Solution steps

\int_{1}^{7} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{l n (7)} u d u

= \int_{0}^{l n (7)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{l n (7)}

= [\frac{u ^{2}}{2}]_{0}^{l n (7)}

Compute the boundaries:

\frac{ln ^{2} ( 7 )}{2}

= \frac{ln ^{2} ( 7 )}{2}

x \to 1 lim (3 x^{2})

\frac{\partial}{\partial x} (y^{5 x})

\frac{d}{d x} (4 - e^{x})

\frac{d}{d x} (\frac{( 4 x ^{2} + 2 x + 2 )}{x})

y^{^{''}} + 6 y^{^{'}} = 162 e^{3 t}, y (0) = 6, y^{^{'}} (0) = 7

What is the integral from 1 to 7 of (ln(x))/x ?
The integral from 1 to 7 of (ln(x))/x is (ln^2(7))/2