What is the integral from 3 to 5 of 1/(sqrt(|x-1|)) ?

The integral from 3 to 5 of 1/(sqrt(|x-1|)) is 4-2sqrt(2)

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integral from 3 to 5 of 1/(sqrt(|x-1|))

\int_{3}^{5} \frac{1}{∣ x - 1 ∣} d x

4 - 22

Decimal Notation

1.17157 \dots

Solution steps

\int_{3}^{5} \frac{1}{∣ x - 1 ∣} d x

Eliminate Absolutes

= \int_{3}^{5} \frac{1}{x - 1} d x

Apply u-substitution

: \int_{2}^{2} 2 d u

= \int_{2}^{2} 2 d u

Integral of a constant:

\int a d x = a x

= [2 u]_{2}^{2}

Compute the boundaries:

4 - 22

= 4 - 22

\int_{6}^{10} 3 x^{2} + 1 d x

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

\int_{0}^{t} e^{- 2 u} sin (u) d u

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

\int_{1}^{n} \frac{x ^{3}}{n ^{4}} d x

What is the integral from 3 to 5 of 1/(sqrt(|x-1|)) ?
The integral from 3 to 5 of 1/(sqrt(|x-1|)) is 4-2sqrt(2)