What is the integral from 5 to 7 of 1/(x-4) ?

The integral from 5 to 7 of 1/(x-4) is ln(3)

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integral from 5 to 7 of 1/(x-4)

\int_{5}^{7} \frac{1}{x - 4} d x

ln (3)

Decimal

1.09861 \dots

Solution steps

\int_{5}^{7} \frac{1}{x - 4} d x

Apply u-substitution

: \int_{1}^{3} \frac{1}{u} d u

= \int_{1}^{3} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= ln (3)

\int_{- 2}^{0} 3 x d x

\int_{0}^{x^{2}} x d x

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

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

\int_{1}^{7} x d x

What is the integral from 5 to 7 of 1/(x-4) ?
The integral from 5 to 7 of 1/(x-4) is ln(3)