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

The integral from e to 2e of ln(x) is 2eln(2e)-2e

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integral from e to 2e of ln(x)

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

2 e ln (2 e) - 2 e

Decimal Notation

3.76833 \dots

Solution steps

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

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{e}^{2 e}

= [x ln (x) - \int 1 d x]_{e}^{2 e}

\int 1 d x = x

= [x ln (x) - x]_{e}^{2 e}

Compute the boundaries:

2 e ln (2 e) - 2 e

= 2 e ln (2 e) - 2 e

\int_{0}^{3} \frac{x ^{2}}{x ^{3} + 9} d x

\int_{0}^{x} (x - y) d y

\int_{0}^{x} \frac{x ^{2}}{9} d x

\int_{1}^{e} \frac{9}{x} d x

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

What is the integral from e to 2e of ln(x) ?
The integral from e to 2e of ln(x) is 2eln(2e)-2e