What is the integral from 0 to 3 of 1/((x-1)^{3/2)} ?

The integral from 0 to 3 of 1/((x-1)^{3/2)} is diverges

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integral from 0 to 3 of 1/((x-1)^{3/2)}

\int_{0}^{3} \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x

diverges

Solution steps

\int_{0}^{3} \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x

Adjust integral based on undefined pointsThere is an undefined point within the boundaries at

: 1

= \int_{0}^{1} \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x + \int_{1}^{3} \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x

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

diverges

= diverges

What is the integral from 0 to 3 of 1/((x-1)^{3/2)} ?
The integral from 0 to 3 of 1/((x-1)^{3/2)} is diverges