What is the integral from 1 to 7 of 7/(sqrt(x-6)) ?

The integral from 1 to 7 of 7/(sqrt(x-6)) is -14sqrt(5)i+14

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integral from 1 to 7 of 7/(sqrt(x-6))

\int_{1}^{7} \frac{7}{x - 6} d x

- 145 i + 14

Solution steps

\int_{1}^{7} \frac{7}{x - 6} d x

Find undefined (singularity) points:

x = 6

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_{1}^{6} \frac{7}{x - 6} d x + \int_{6}^{7} \frac{7}{x - 6} d x

\int_{1}^{6} \frac{7}{x - 6} d x = - 145 i

\int_{6}^{7} \frac{7}{x - 6} d x = 14

= - 145 i + 14

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What is the integral from 1 to 7 of 7/(sqrt(x-6)) ?
The integral from 1 to 7 of 7/(sqrt(x-6)) is -14sqrt(5)i+14