What is the integral from 3 to 6 of 15ln(x+5) ?

The integral from 3 to 6 of 15ln(x+5) is 15(11ln(11)-3-24ln(2))

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integral from 3 to 6 of 15ln(x+5)

\int_{3}^{6} 15 ln (x + 5) d x

15 (11 ln (11) - 3 - 24 ln (2))

Decimal

101.11973 \dots

Solution steps

\int_{3}^{6} 15 ln (x + 5) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15 \cdot \int_{3}^{6} ln (x + 5) d x

Apply u-substitution

: \int_{8}^{11} ln (u) d u

= 15 \cdot \int_{8}^{11} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{8}^{11}

= 15 [u ln (u) - \int 1 d u]_{8}^{11}

\int 1 d u = u

= 15 [u ln (u) - u]_{8}^{11}

Compute the boundaries:

11 ln (11) - 3 - 24 ln (2)

= 15 (11 ln (11) - 3 - 24 ln (2))

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What is the integral from 3 to 6 of 15ln(x+5) ?
The integral from 3 to 6 of 15ln(x+5) is 15(11ln(11)-3-24ln(2))