What is the integral from 1 to 9 of 1/((x-1)^{5/2)} ?

The integral from 1 to 9 of 1/((x-1)^{5/2)} is diverges

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integral from 1 to 9 of 1/((x-1)^{5/2)}

\int_{1}^{9} \frac{1}{( x - 1 ) ^{\frac{5}{2}}} d x

diverges

Solution steps

\int_{1}^{9} \frac{1}{( x - 1 ) ^{\frac{5}{2}}} d x

Apply u-substitution

: \int_{0}^{8} \frac{1}{u ^{\frac{5}{2}}} d u

= \int_{0}^{8} \frac{1}{u ^{\frac{5}{2}}} d u

Apply the Power Rule

: [- \frac{2}{3 u ^{\frac{3}{2}}}]_{0}^{8}

= [- \frac{2}{3 u ^{\frac{3}{2}}}]_{0}^{8}

Compute the boundaries:

diverges

= diverges

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What is the integral from 1 to 9 of 1/((x-1)^{5/2)} ?
The integral from 1 to 9 of 1/((x-1)^{5/2)} is diverges