What is the integral from 0 to 1 of 1/(5x-10) ?

The integral from 0 to 1 of 1/(5x-10) is -1/5 ln(2)

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integral from 0 to 1 of 1/(5x-10)

\int_{0}^{1} \frac{1}{5 x - 10} d x

- \frac{1}{5} ln (2)

Decimal Notation

- 0.13862 \dots

Solution steps

\int_{0}^{1} \frac{1}{5 x - 10} d x

Apply u-substitution

: \int_{- 10}^{- 5} \frac{1}{5 u} d u

= \int_{- 10}^{- 5} \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{- 10}^{- 5} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} [ln ∣ u ∣]_{- 10}^{- 5}

Compute the boundaries:

ln (5) - ln (10)

= \frac{1}{5} (ln (5) - ln (10))

Simplify

= - \frac{1}{5} ln (2)

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What is the integral from 0 to 1 of 1/(5x-10) ?
The integral from 0 to 1 of 1/(5x-10) is -1/5 ln(2)