What is the integral from 1 to 5 of ln(x-1) ?

The integral from 1 to 5 of ln(x-1) is 8ln(2)-4

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integral from 1 to 5 of ln(x-1)

\int_{1}^{5} ln (x - 1) d x

8 ln (2) - 4

Decimal Notation

1.54517 \dots

Solution steps

\int_{1}^{5} ln (x - 1) d x

Apply u-substitution

: \int_{0}^{4} ln (u) d u

= \int_{0}^{4} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{0}^{4}

= [u ln (u) - \int 1 d u]_{0}^{4}

\int 1 d u = u

= [u ln (u) - u]_{0}^{4}

Compute the boundaries:

8 ln (2) - 4

= 8 ln (2) - 4

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What is the integral from 1 to 5 of ln(x-1) ?
The integral from 1 to 5 of ln(x-1) is 8ln(2)-4