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

The integral from e to e^3 of (ln(x))/x is 4

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

\int_{e}^{e^{3}} \frac{ln ( x )}{x} d x

4

Solution steps

\int_{e}^{e^{3}} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{1}^{3} u d u

= \int_{1}^{3} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{1}^{3}

= [\frac{u ^{2}}{2}]_{1}^{3}

Compute the boundaries:

4

= 4

\int_{2}^{2} 1

\int_{x^{2}}^{x} \frac{x}{y} d y

\int_{1}^{2} \frac{x ^{2} + 5}{x} d x

\int_{- 2}^{1} x + 1 d x

\int_{1}^{2} f (t) d t

What is the integral from e to e^3 of (ln(x))/x ?
The integral from e to e^3 of (ln(x))/x is 4