What is the integral from 1 to 2 of 1/(8-3x) ?

The integral from 1 to 2 of 1/(8-3x) is 1/3 (ln(5)-ln(2))

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integral from 1 to 2 of 1/(8-3x)

\int_{1}^{2} \frac{1}{8 - 3 x} d x

\frac{1}{3} (ln (5) - ln (2))

Decimal

0.30543 \dots

Solution steps

\int_{1}^{2} \frac{1}{8 - 3 x} d x

Apply u-substitution

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

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

= - (- \frac{1}{3} \cdot \int_{2}^{5} \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{3} [ln ∣ u ∣]_{2}^{5})

Simplify

= \frac{1}{3} [ln ∣ u ∣]_{2}^{5}

Compute the boundaries:

ln (5) - ln (2)

= \frac{1}{3} (ln (5) - ln (2))

What is the integral from 1 to 2 of 1/(8-3x) ?
The integral from 1 to 2 of 1/(8-3x) is 1/3 (ln(5)-ln(2))