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

The integral from-5 to 5 of ln(x+6) is 11ln(11)-10

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integral from-5 to 5 of ln(x+6)

\int_{- 5}^{5} ln (x + 6) d x

11 ln (11) - 10

Decimal

16.37684 \dots

Solution steps

\int_{- 5}^{5} ln (x + 6) d x

Apply u-substitution

: \int_{1}^{11} ln (u) d u

= \int_{1}^{11} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{1}^{11}

= [u ln (u) - \int 1 d u]_{1}^{11}

\int 1 d u = u

= [u ln (u) - u]_{1}^{11}

Compute the boundaries:

11 ln (11) - 10

= 11 ln (11) - 10

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What is the integral from-5 to 5 of ln(x+6) ?
The integral from-5 to 5 of ln(x+6) is 11ln(11)-10