What is the integral from e to e^2 of (ln(x))/x ?

The integral from e to e^2 of (ln(x))/x is 3/2

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integral from e to e^2 of (ln(x))/x

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

\frac{3}{2}

Decimal

1.5

Solution steps

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

Apply u-substitution

: \int_{1}^{2} u d u

= \int_{1}^{2} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{1}^{2}

= [\frac{u ^{2}}{2}]_{1}^{2}

Compute the boundaries:

\frac{3}{2}

= \frac{3}{2}

\int_{1}^{x} sin (t^{2}) d t

\int_{0}^{1} x^{2} e^{- x^{3}} d x

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{3}} d x

\int_{0}^{3} x e^{2 x} d x

\int_{0}^{4} \frac{1}{( x - 3 ) ^{2}} d x

What is the integral from e to e^2 of (ln(x))/x ?
The integral from e to e^2 of (ln(x))/x is 3/2