What is the integral from-2 to 1 of 3/(12x-13) ?

The integral from-2 to 1 of 3/(12x-13) is -1/4 ln(37)

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integral from-2 to 1 of 3/(12x-13)

\int_{- 2}^{1} \frac{3}{12 x - 13} d x

- \frac{1}{4} ln (37)

Decimal Notation

- 0.90272 \dots

Solution steps

\int_{- 2}^{1} \frac{3}{12 x - 13} d x

Take the constant out:

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

= 3 \cdot \int_{- 2}^{1} \frac{1}{12 x - 13} d x

Apply u-substitution

: \int_{- 37}^{- 1} \frac{1}{12 u} d u

= 3 \cdot \int_{- 37}^{- 1} \frac{1}{12 u} d u

Take the constant out:

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

= 3 \cdot \frac{1}{12} \cdot \int_{- 37}^{- 1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{12} [ln ∣ u ∣]_{- 37}^{- 1}

Simplify

3 \cdot \frac{1}{12} [ln ∣ u ∣]_{- 37}^{- 1} : \frac{1}{4} [ln ∣ u ∣]_{- 37}^{- 1}

= \frac{1}{4} [ln ∣ u ∣]_{- 37}^{- 1}

Compute the boundaries:

- ln (37)

= \frac{1}{4} (- ln (37))

Simplify

= - \frac{1}{4} ln (37)

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What is the integral from-2 to 1 of 3/(12x-13) ?
The integral from-2 to 1 of 3/(12x-13) is -1/4 ln(37)