What is the integral from 6 to infinity of 1/((x-5)^{3/2)} ?

The integral from 6 to infinity of 1/((x-5)^{3/2)} is 2

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integral from 6 to infinity of 1/((x-5)^{3/2)}

\int_{6}^{\infty} \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x

2

Solution steps

\int_{6}^{\infty} \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x

Compute the indefinite integral:

\int \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x = - \frac{2}{( x - 5 ) ^{\frac{1}{2}}} + C

Compute the boundaries:

\int_{6}^{\infty} \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x = 0 - (- 2)

= 0 - (- 2)

Simplify

= 2

\int_{0}^{5} x^{2} + 25 d x

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What is the integral from 6 to infinity of 1/((x-5)^{3/2)} ?
The integral from 6 to infinity of 1/((x-5)^{3/2)} is 2