What is the integral from 3 to 8 of ln(1+x) ?

The integral from 3 to 8 of ln(1+x) is 18ln(3)-5-8ln(2)

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integral from 3 to 8 of ln(1+x)

\int_{3}^{8} ln (1 + x) d x

18 ln (3) - 5 - 8 ln (2)

Decimal

9.22984 \dots

Solution steps

\int_{3}^{8} ln (1 + x) d x

Apply u-substitution

: \int_{4}^{9} ln (u) d u

= \int_{4}^{9} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{4}^{9}

= [u ln (u) - \int 1 d u]_{4}^{9}

\int 1 d u = u

= [u ln (u) - u]_{4}^{9}

Compute the boundaries:

18 ln (3) - 5 - 8 ln (2)

= 18 ln (3) - 5 - 8 ln (2)

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What is the integral from 3 to 8 of ln(1+x) ?
The integral from 3 to 8 of ln(1+x) is 18ln(3)-5-8ln(2)