What is the integral from 1 to 6 of ln(1+x) ?

The integral from 1 to 6 of ln(1+x) is 7ln(7)-5-2ln(2)

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integral from 1 to 6 of ln(1+x)

\int_{1}^{6} ln (1 + x) d x

7 ln (7) - 5 - 2 ln (2)

Decimal

7.23507 \dots

Solution steps

\int_{1}^{6} ln (1 + x) d x

Apply u-substitution

: \int_{2}^{7} ln (u) d u

= \int_{2}^{7} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{2}^{7}

= [u ln (u) - \int 1 d u]_{2}^{7}

\int 1 d u = u

= [u ln (u) - u]_{2}^{7}

Compute the boundaries:

7 ln (7) - 5 - 2 ln (2)

= 7 ln (7) - 5 - 2 ln (2)

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What is the integral from 1 to 6 of ln(1+x) ?
The integral from 1 to 6 of ln(1+x) is 7ln(7)-5-2ln(2)