What is the integral from 9 to 10 of 1/((x-9)^{5/4)} ?

The integral from 9 to 10 of 1/((x-9)^{5/4)} is diverges

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integral from 9 to 10 of 1/((x-9)^{5/4)}

\int_{9}^{10} \frac{1}{( x - 9 ) ^{\frac{5}{4}}} d x

diverges

Solution steps

\int_{9}^{10} \frac{1}{( x - 9 ) ^{\frac{5}{4}}} d x

Apply u-substitution

: \int_{0}^{1} \frac{1}{u ^{\frac{5}{4}}} d u

= \int_{0}^{1} \frac{1}{u ^{\frac{5}{4}}} d u

Apply the Power Rule

: [- \frac{4}{u ^{\frac{1}{4}}}]_{0}^{1}

= [- \frac{4}{u ^{\frac{1}{4}}}]_{0}^{1}

Compute the boundaries:

diverges

= diverges

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x \to 3 lim (- x + 2)

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What is the integral from 9 to 10 of 1/((x-9)^{5/4)} ?
The integral from 9 to 10 of 1/((x-9)^{5/4)} is diverges