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

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

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integral from 0 to 1 of x/(sqrt(x^2-1))

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

- i

Solution steps

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

Compute the indefinite integral:

\int \frac{x}{x ^{2} - 1} d x = x^{2} - 1 + C

Compute the boundaries:

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x = 0 - i

= 0 - i

Simplify

= - i

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