What is the integral from 0 to e of ln(x) ?

The integral from 0 to e of ln(x) is 0

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integral from 0 to e of ln(x)

\int_{0}^{e} ln (x) d x

0

Solution steps

\int_{0}^{e} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{e}

= [x ln (x) - \int 1 d x]_{0}^{e}

\int 1 d x = x

= [x ln (x) - x]_{0}^{e}

Compute the boundaries:

0

= 0

\int (1 + e)^{x} d x

\frac{d y}{d x} = \frac{y ^{3}}{x ^{2}}

\int x^{3} (1 - x^{4})^{5} d x

\int (\frac{7}{1 - x ^{2}}) d x

\int (\frac{1}{1 + x ^{2}})^{2} d x

What is the integral from 0 to e of ln(x) ?
The integral from 0 to e of ln(x) is 0