What is the integral from 3 to 7 of 15ln(x+5) ?

The integral from 3 to 7 of 15ln(x+5) is 15(12ln(3)-4)

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integral from 3 to 7 of 15ln(x+5)

\int_{3}^{7} 15 ln (x + 5) d x

15 (12 ln (3) - 4)

Decimal

137.75021 \dots

Solution steps

\int_{3}^{7} 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}^{7} ln (x + 5) d x

Apply u-substitution

: \int_{8}^{12} ln (u) d u

= 15 \cdot \int_{8}^{12} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{8}^{12}

= 15 [u ln (u) - \int 1 d u]_{8}^{12}

\int 1 d u = u

= 15 [u ln (u) - u]_{8}^{12}

Compute the boundaries:

12 ln (12) - 4 - 24 ln (2)

= 15 (12 ln (12) - 4 - 24 ln (2))

Simplify

= 15 (12 ln (3) - 4)

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What is the integral from 3 to 7 of 15ln(x+5) ?
The integral from 3 to 7 of 15ln(x+5) is 15(12ln(3)-4)