What is the integral from 1 to 6 of 2/(x-11) ?

The integral from 1 to 6 of 2/(x-11) is -2ln(2)

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integral from 1 to 6 of 2/(x-11)

\int_{1}^{6} \frac{2}{x - 11} d x

- 2 ln (2)

Decimal

- 1.38629 \dots

Solution steps

\int_{1}^{6} \frac{2}{x - 11} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{6} \frac{1}{x - 11} d x

Apply u-substitution

: \int_{- 10}^{- 5} \frac{1}{u} d u

= 2 \cdot \int_{- 10}^{- 5} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{- 10}^{- 5}

Compute the boundaries:

ln (5) - ln (10)

= 2 (ln (5) - ln (10))

Simplify

= - 2 ln (2)

\frac{d x}{d t} + 4 \cdot 1 0^{- 4} x = 8 \cdot 1 0^{- 5}, x (0) = 1

f (x) = 3 x^{2} - 5 x + 1

(4 x - 3)^{\frac{1}{2}}

ln (1 + x), 0

y^{^{'}} + 3 y = e^{- 3 t}

What is the integral from 1 to 6 of 2/(x-11) ?
The integral from 1 to 6 of 2/(x-11) is -2ln(2)