What is the integral from 4 to 6 of 1/(x-2) ?

The integral from 4 to 6 of 1/(x-2) is ln(2)

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integral from 4 to 6 of 1/(x-2)

\int_{4}^{6} \frac{1}{x - 2} d x

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

\int_{4}^{6} \frac{1}{x - 2} d x

Apply u-substitution

: \int_{2}^{4} \frac{1}{u} d u

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2}^{4}

Compute the boundaries:

ln (2)

= ln (2)

\int_{1}^{5} \frac{3 t}{e ^{2 t}} d t

\int_{0}^{4} e^{(x - 2)^{4}} d x

\int_{0}^{2} (3 x - 1)^{3} d x

\int_{0}^{1} (2 t)^{2} d t

\int_{2}^{5} x (x - 3)^{4} d x

What is the integral from 4 to 6 of 1/(x-2) ?
The integral from 4 to 6 of 1/(x-2) is ln(2)