What is the integral from 1 to 5 of (ln(x))/x ?

The integral from 1 to 5 of (ln(x))/x is (ln^2(5))/2

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integral from 1 to 5 of (ln(x))/x

\int_{1}^{5} \frac{ln ( x )}{x} d x

\frac{ln ^{2} ( 5 )}{2}

Decimal Notation

1.29514 \dots

Solution steps

\int_{1}^{5} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{l n (5)} u d u

= \int_{0}^{l n (5)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{l n (5)}

= [\frac{u ^{2}}{2}]_{0}^{l n (5)}

Compute the boundaries:

\frac{ln ^{2} ( 5 )}{2}

= \frac{ln ^{2} ( 5 )}{2}

\int_{- \infty}^{0} \frac{1}{5 - 9 x} d x

3 e^{4 t}

4 y^{^{''}} - 4 y^{^{'}} - 3 y = cos (2 x)

\frac{d}{d a} (tan (a) + cot (a))

8 y^{^{''}} + 31 y = 0

What is the integral from 1 to 5 of (ln(x))/x ?
The integral from 1 to 5 of (ln(x))/x is (ln^2(5))/2