What is the integral from 3 to 6 of ln(x) ?

The integral from 3 to 6 of ln(x) is 3ln(12)-3

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integral from 3 to 6 of ln(x)

\int_{3}^{6} ln (x) d x

3 ln (12) - 3

Decimal

4.45471 \dots

Solution steps

\int_{3}^{6} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{3}^{6}

= [x ln (x) - \int 1 d x]_{3}^{6}

\int 1 d x = x

= [x ln (x) - x]_{3}^{6}

Compute the boundaries:

6 ln (6) - 3 - 3 ln (3)

= 6 ln (6) - 3 - 3 ln (3)

Simplify

= 3 ln (12) - 3

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What is the integral from 3 to 6 of ln(x) ?
The integral from 3 to 6 of ln(x) is 3ln(12)-3