What is the integral from 2 to 3 of-ln(x-2) ?

The integral from 2 to 3 of-ln(x-2) is 1

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integral from 2 to 3 of-ln(x-2)

\int_{2}^{3} - ln (x - 2) d x

1

Solution steps

\int_{2}^{3} - ln (x - 2) d x

Take the constant out:

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

= - \int_{2}^{3} ln (x - 2) d x

Apply u-substitution

: \int_{0}^{1} ln (u) d u

= - \int_{0}^{1} ln (u) d u

Apply Integration By Parts

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

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

\int 1 d u = u

= - [u ln (u) - u]_{0}^{1}

Compute the boundaries:

- 1

= - (- 1)

Simplify

= 1

\int_{1}^{n} \frac{x ^{3}}{n ^{4}} d x

\int_{- 1}^{3} (x^{2} + x) d x

\int_{0}^{0.99} \frac{1}{1 - x} d x

\int_{2}^{\infty} \frac{4}{x ^{4}} d x

\int_{0}^{9} 300 e^{- 0.11 x} d x

What is the integral from 2 to 3 of-ln(x-2) ?
The integral from 2 to 3 of-ln(x-2) is 1