What is the integral from 2 to 7 of ln(1+x) ?

The integral from 2 to 7 of ln(1+x) is 24ln(2)-5-3ln(3)

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integral from 2 to 7 of ln(1+x)

\int_{2}^{7} ln (1 + x) d x

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

Decimal

8.33969 \dots

Solution steps

\int_{2}^{7} ln (1 + x) d x

Apply u-substitution

: \int_{3}^{8} ln (u) d u

= \int_{3}^{8} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{3}^{8}

= [u ln (u) - \int 1 d u]_{3}^{8}

\int 1 d u = u

= [u ln (u) - u]_{3}^{8}

Compute the boundaries:

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

= 24 ln (2) - 5 - 3 ln (3)

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What is the integral from 2 to 7 of ln(1+x) ?
The integral from 2 to 7 of ln(1+x) is 24ln(2)-5-3ln(3)