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 8

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

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

8

Solution steps

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

Eliminate Absolutes

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

\int_{- 3}^{1} \frac{1}{- x + 1} d x = 4

\int_{1}^{5} \frac{1}{x - 1} d x = 4

= 4 + 4

Simplify

= 8

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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 8