What is the integral from 0 to 0.5 of ln(x+1) ?

The integral from 0 to 0.5 of ln(x+1) is 0.10819…

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integral from 0 to 0.5 of ln(x+1)

\int_{0}^{0.5} ln (x + 1) d x

0.10819 \dots

Solution steps

\int_{0}^{0.5} ln (x + 1) d x

Apply u-substitution

: \int_{1}^{1.5} ln (u) d u

= \int_{1}^{1.5} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{1}^{1.5}

= [u ln (u) - \int 1 d u]_{1}^{1.5}

\int 1 d u = u

= [u ln (u) - u]_{1}^{1.5}

Compute the boundaries:

0.10819 \dots

= 0.10819 \dots

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What is the integral from 0 to 0.5 of ln(x+1) ?
The integral from 0 to 0.5 of ln(x+1) is 0.10819…