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

The integral from 1 to e of (ln(x)) is 1

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integral from 1 to e of (ln(x))

\int_{1}^{e} (ln (x)) d x

1

Solution steps

\int_{1}^{e} ln (x) d x

Apply Integration By Parts

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

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

\int 1 d x = x

= [x ln (x) - x]_{1}^{e}

Compute the boundaries:

1

= 1

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

\int_{- 2}^{3} x^{3} - x^{2} - 6 x d x

What is the integral from 1 to e of (ln(x)) ?
The integral from 1 to e of (ln(x)) is 1