What is the integral from 3 to 7 of 1/(2x-5) ?

The integral from 3 to 7 of 1/(2x-5) is ln(3)

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integral from 3 to 7 of 1/(2x-5)

\int_{3}^{7} \frac{1}{2 x - 5} d x

ln (3)

Decimal

1.09861 \dots

Solution steps

\int_{3}^{7} \frac{1}{2 x - 5} d x

Apply u-substitution

: \int_{1}^{9} \frac{1}{2 u} d u

= \int_{1}^{9} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{9} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= \frac{1}{2} \cdot 2 ln (3)

Simplify

= ln (3)

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What is the integral from 3 to 7 of 1/(2x-5) ?
The integral from 3 to 7 of 1/(2x-5) is ln(3)