What is the integral from-5 to-2 of 3 1/x ?

The integral from-5 to-2 of 3 1/x is 3(ln(2)-ln(5))

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integral from-5 to-2 of 3 1/x

\int_{- 5}^{- 2} 3 \frac{1}{x} d x

3 (ln (2) - ln (5))

Decimal Notation

- 2.74887 \dots

Solution steps

\int_{- 5}^{- 2} 3 \cdot \frac{1}{x} d x

Take the constant out:

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

= 3 \cdot \int_{- 5}^{- 2} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{- 5}^{- 2}

Compute the boundaries:

ln (2) - ln (5)

= 3 (ln (2) - ln (5))

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What is the integral from-5 to-2 of 3 1/x ?
The integral from-5 to-2 of 3 1/x is 3(ln(2)-ln(5))