What is the integral from 0 to 1 of 2/(x-2) ?

The integral from 0 to 1 of 2/(x-2) is -2ln(2)

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integral from 0 to 1 of 2/(x-2)

\int_{0}^{1} \frac{2}{x - 2} d x

- 2 ln (2)

Decimal

- 1.38629 \dots

Solution steps

\int_{0}^{1} \frac{2}{x - 2} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} \frac{1}{x - 2} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{- 2}^{- 1}

Compute the boundaries:

- ln (2)

= 2 (- ln (2))

Simplify

= - 2 ln (2)

\frac{d}{d x} (\frac{1}{1 + 2 x})

\frac{d}{d x} (9 + 5 x)

\frac{d}{d x} (2 x^{- 7 3 x})

n = 1 \sum \infty n! 2^{n} n^{- n}

1 + 4 x^{2}

What is the integral from 0 to 1 of 2/(x-2) ?
The integral from 0 to 1 of 2/(x-2) is -2ln(2)