What is the integral from 3 to 6 of 2/(x-2) ?

The integral from 3 to 6 of 2/(x-2) is 4ln(2)

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integral from 3 to 6 of 2/(x-2)

\int_{3}^{6} \frac{2}{x - 2} d x

4 ln (2)

Decimal Notation

2.77258 \dots

Solution steps

\int_{3}^{6} \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_{3}^{6} \frac{1}{x - 2} d x

Apply u-substitution

: \int_{1}^{4} \frac{1}{u} d u

= 2 \cdot \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 \cdot 2 ln (2)

Simplify

= 4 ln (2)

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

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\int_{0}^{5} 2 x^{3} - 3 x^{2} + 4 x + 1 d x

\int_{0}^{1.3} \frac{1}{6} x d x

\int_{- π}^{0} (x - π) sin (n x) d x

What is the integral from 3 to 6 of 2/(x-2) ?
The integral from 3 to 6 of 2/(x-2) is 4ln(2)