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

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

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integral from-3 to-1 of 2/x

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

- 2 ln (3)

Decimal

- 2.19722 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{- 3}^{- 1}

Compute the boundaries:

- ln (3)

= 2 (- ln (3))

Simplify

= - 2 ln (3)

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