What is the integral from 5 to 7 of 3/((x-6)^{4/5)} ?

The integral from 5 to 7 of 3/((x-6)^{4/5)} is 30

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integral from 5 to 7 of 3/((x-6)^{4/5)}

\int_{5}^{7} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} d x

30

Solution steps

\int_{5}^{7} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} 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_{5}^{6} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} d x + \int_{6}^{7} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} d x

\int_{5}^{6} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} d x = - 15 (- 1)^{\frac{1}{5}}

\int_{6}^{7} \frac{3}{( x - 6 ) ^{\frac{4}{5}}} d x = 15

= - 15 (- 1)^{\frac{1}{5}} + 15

Simplify

- 15 (- 1)^{\frac{1}{5}} + 15 : 30

= 30

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What is the integral from 5 to 7 of 3/((x-6)^{4/5)} ?
The integral from 5 to 7 of 3/((x-6)^{4/5)} is 30