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

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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

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\int_{0}^{x} \frac{x ^{- \frac{1}{2}}}{6} d x

\int_{0}^{l n (e)} x e^{2 x} d x

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