What is the integral from 2 to 5 of 1/((x+4)) ?

The integral from 2 to 5 of 1/((x+4)) is ln(3/2)

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integral from 2 to 5 of 1/((x+4))

\int_{2}^{5} \frac{1}{( x + 4 )} d x

ln (\frac{3}{2})

Decimal

0.40546 \dots

Solution steps

\int_{2}^{5} \frac{1}{x + 4} d x

Apply u-substitution

: \int_{6}^{9} \frac{1}{u} d u

= \int_{6}^{9} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{6}^{9}

Compute the boundaries:

2 ln (3) - ln (6)

= 2 ln (3) - ln (6)

Simplify

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

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What is the integral from 2 to 5 of 1/((x+4)) ?
The integral from 2 to 5 of 1/((x+4)) is ln(3/2)