What is the integral from 4 to 5 of 2/((x-3)) ?

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

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integral from 4 to 5 of 2/((x-3))

\int_{4}^{5} \frac{2}{( x - 3 )} d x

2 ln (2)

Decimal

1.38629 \dots

Solution steps

\int_{4}^{5} \frac{2}{x - 3} d x

Take the constant out:

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

= 2 \cdot \int_{4}^{5} \frac{1}{x - 3} d x

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{2}

Compute the boundaries:

ln (2)

= 2 ln (2)

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