What is the integral from-10 to-3 of 1/(x+2) ?

The integral from-10 to-3 of 1/(x+2) is -3ln(2)

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integral from-10 to-3 of 1/(x+2)

\int_{- 10}^{- 3} \frac{1}{x + 2} d x

- 3 ln (2)

Decimal

- 2.07944 \dots

Solution steps

\int_{- 10}^{- 3} \frac{1}{x + 2} d x

Apply u-substitution

: \int_{- 8}^{- 1} \frac{1}{u} d u

= \int_{- 8}^{- 1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 8}^{- 1}

Compute the boundaries:

- 3 ln (2)

= - 3 ln (2)

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What is the integral from-10 to-3 of 1/(x+2) ?
The integral from-10 to-3 of 1/(x+2) is -3ln(2)