What is the integral from 6 to 13 of ln(x-6) ?

The integral from 6 to 13 of ln(x-6) is 7ln(7)-7

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integral from 6 to 13 of ln(x-6)

\int_{6}^{13} ln (x - 6) d x

7 ln (7) - 7

Decimal Notation

6.62137 \dots

Solution steps

\int_{6}^{13} ln (x - 6) d x

Apply u-substitution

: \int_{0}^{7} ln (u) d u

= \int_{0}^{7} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{0}^{7}

= [u ln (u) - \int 1 d u]_{0}^{7}

\int 1 d u = u

= [u ln (u) - u]_{0}^{7}

Compute the boundaries:

7 ln (7) - 7

= 7 ln (7) - 7

x \to 0 lim (25)

\frac{d}{d x} (arctan (10 x))

\frac{d}{d x} (ln (x^{2} - 9))

x^{2} + (\frac{1}{2} x - 5)^{2}

What is the integral from 6 to 13 of ln(x-6) ?
The integral from 6 to 13 of ln(x-6) is 7ln(7)-7