What is the integral from 0 to 3 of 2/(x+1) ?

The integral from 0 to 3 of 2/(x+1) is 4ln(2)

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integral from 0 to 3 of 2/(x+1)

\int_{0}^{3} \frac{2}{x + 1} d x

4 ln (2)

Decimal

2.77258 \dots

Solution steps

\int_{0}^{3} \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}^{3} \frac{1}{x + 1} d x

Apply u-substitution

= 2 \cdot \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 \cdot 2 ln (2)

Simplify

= 4 ln (2)

What is the integral from 0 to 3 of 2/(x+1) ?
The integral from 0 to 3 of 2/(x+1) is 4ln(2)