What is the integral from 3 to 5 of 1/(sqrt(x-4)) ?

The integral from 3 to 5 of 1/(sqrt(x-4)) is -2i+2

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integral from 3 to 5 of 1/(sqrt(x-4))

\int_{3}^{5} \frac{1}{x - 4} d x

- 2 i + 2

Solution steps

\int_{3}^{5} \frac{1}{x - 4} d x

Find undefined (singularity) points:

x = 4

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

\int_{3}^{4} \frac{1}{x - 4} d x = - 2 i

\int_{4}^{5} \frac{1}{x - 4} d x = 2

= - 2 i + 2

\int_{0}^{1} 5 x (1 - x)^{4} d x

\int_{0}^{1} a x + b d x

\int_{- 1}^{1} sec^{3} (x) tan^{3} (x) d x

\int_{0}^{\frac{3 π}{4}} tan (\frac{x}{3}) d x

\int_{- 2}^{1} (5 x^{2} - 7 x + 3) d x

What is the integral from 3 to 5 of 1/(sqrt(x-4)) ?
The integral from 3 to 5 of 1/(sqrt(x-4)) is -2i+2