What is the integral from 1 to 5 of 1/(x-6) ?

The integral from 1 to 5 of 1/(x-6) is -ln(5)

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integral from 1 to 5 of 1/(x-6)

\int_{1}^{5} \frac{1}{x - 6} d x

- ln (5)

Decimal Notation

- 1.60943 \dots

Solution steps

\int_{1}^{5} \frac{1}{x - 6} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 5}^{- 1}

Compute the boundaries:

- ln (5)

= - ln (5)

\int_{- 2}^{x} (26 t^{2} - 25 t) d t

\int_{0}^{t} e^{- 2 t} d t

\int_{- 1}^{0} x e^{- x} d x

\int_{e}^{e^{3}} \frac{ln ( x )}{x} d x

\int_{2}^{2} 1

What is the integral from 1 to 5 of 1/(x-6) ?
The integral from 1 to 5 of 1/(x-6) is -ln(5)