What is the integral from 0 to 2 of ln(x+4) ?

The integral from 0 to 2 of ln(x+4) is ln(729/4)-2

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integral from 0 to 2 of ln(x+4)

\int_{0}^{2} ln (x + 4) d x

ln (\frac{729}{4}) - 2

Decimal

3.20537 \dots

Solution steps

\int_{0}^{2} ln (x + 4) d x

Apply u-substitution

: \int_{4}^{6} ln (u) d u

= \int_{4}^{6} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{4}^{6}

= [u ln (u) - \int 1 d u]_{4}^{6}

\int 1 d u = u

= [u ln (u) - u]_{4}^{6}

Compute the boundaries:

6 ln (6) - 2 - 8 ln (2)

= 6 ln (6) - 2 - 8 ln (2)

Simplify

= ln (\frac{729}{4}) - 2

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What is the integral from 0 to 2 of ln(x+4) ?
The integral from 0 to 2 of ln(x+4) is ln(729/4)-2