What is the integral from 3 to 5 of 1/(x+1) ?

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

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integral from 3 to 5 of 1/(x+1)

\int_{3}^{5} \frac{1}{x + 1} d x

ln (\frac{3}{2})

Decimal

0.40546 \dots

Solution steps

\int_{3}^{5} \frac{1}{x + 1} d x

Apply u-substitution

= \int_{4}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{4}^{6}

Compute the boundaries:

ln (6) - 2 ln (2)

= ln (6) - 2 ln (2)

Simplify

= ln (\frac{3}{2})

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