What is the integral from 7 to 8 of 1/((x-7)^{3/2)} ?

The integral from 7 to 8 of 1/((x-7)^{3/2)} is diverges

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integral from 7 to 8 of 1/((x-7)^{3/2)}

\int_{7}^{8} \frac{1}{( x - 7 ) ^{\frac{3}{2}}} d x

diverges

Solution steps

\int_{7}^{8} \frac{1}{( x - 7 ) ^{\frac{3}{2}}} d x

Apply u-substitution

= \int_{0}^{1} \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

= [- \frac{2}{u ^{\frac{1}{2}}}]_{0}^{1}

Compute the boundaries:

diverges

= diverges

What is the integral from 7 to 8 of 1/((x-7)^{3/2)} ?
The integral from 7 to 8 of 1/((x-7)^{3/2)} is diverges