What is the integral from 0 to 4 of 1/(sqrt(x-1)) ?

The integral from 0 to 4 of 1/(sqrt(x-1)) is -2i+2sqrt(3)

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integral from 0 to 4 of 1/(sqrt(x-1))

\int_{0}^{4} \frac{1}{x - 1} d x

- 2 i + 23

Solution steps

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

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

\int_{1}^{4} \frac{1}{x - 1} d x = 23

= - 2 i + 23

\int_{2}^{3} 25 d x

\int_{2}^{4} 1 + 81 x d x

\int_{- \infty}^{1} (x + 4)^{6} d x

\int_{1}^{2} \frac{1}{x ln ^{2} ( x )} d x

\int_{0}^{1} (x + 2) (x + 1)^{9} d x

What is the integral from 0 to 4 of 1/(sqrt(x-1)) ?
The integral from 0 to 4 of 1/(sqrt(x-1)) is -2i+2sqrt(3)