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

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

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

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

- 2 i

Solution steps

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

Apply u-substitution

: \int_{i}^{0} 2 d u

= \int_{i}^{0} 2 d u

Integral of a constant:

\int a d x = a x

= [2 u]_{i}^{0}

Compute the boundaries:

- 2 i

= - 2 i

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\int_{0}^{1} \frac{e ^{x} + 4}{e ^{x} + 4 x} d x

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