What is the integral from 3 to 5 of ln(x) ?

The integral from 3 to 5 of ln(x) is 5ln(5)-2-3ln(3)

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integral from 3 to 5 of ln(x)

\int_{3}^{5} ln (x) d x

5 ln (5) - 2 - 3 ln (3)

Solution steps

\int_{3}^{5} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{3}^{5}

= [x ln (x) - \int 1 d x]_{3}^{5}

\int 1 d x = x

= [x ln (x) - x]_{3}^{5}

Compute the boundaries:

5 ln (5) - 2 - 3 ln (3)

= 5 ln (5) - 2 - 3 ln (3)

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What is the integral from 3 to 5 of ln(x) ?
The integral from 3 to 5 of ln(x) is 5ln(5)-2-3ln(3)