What is the integral from 0 to 5 of (2/(x+1)) ?

The integral from 0 to 5 of (2/(x+1)) is 2ln(6)

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integral from 0 to 5 of (2/(x+1))

\int_{0}^{5} (\frac{2}{x + 1}) d x

2 ln (6)

Decimal

3.58351 \dots

Solution steps

\int_{0}^{5} \frac{2}{x + 1} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{5} \frac{1}{x + 1} d x

Apply u-substitution

: \int_{1}^{6} \frac{1}{u} d u

= 2 \cdot \int_{1}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{6}

Compute the boundaries:

ln (6)

= 2 ln (6)

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What is the integral from 0 to 5 of (2/(x+1)) ?
The integral from 0 to 5 of (2/(x+1)) is 2ln(6)