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

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

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

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

ln (2) - ln (5)

Decimal

- 0.91629 \dots

Solution steps

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

Apply u-substitution

: \int_{- 5}^{- 2} \frac{1}{u} d u

= \int_{- 5}^{- 2} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 5}^{- 2}

Compute the boundaries:

ln (2) - ln (5)

= ln (2) - ln (5)

\int_{1}^{4} (4 x^{3} - 3 x^{2} + 1) d x

\int_{1}^{3} (\frac{ln ^{2} ( 5 )}{2 x}) d x

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

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

\int_{0}^{1} x^{5} (1 - x^{2})^{\frac{3}{2}} d x

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