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 -4i+4

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

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

- 4 i + 4

Solution steps

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

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \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 i

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

= - 4 i + 4

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\int_{0}^{1} [e^{5 x + 3}] 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 -4i+4