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

The integral of 1/((x-5)^{3/2)} is -2/((x-5)^{1/2)}+C

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integral of 1/((x-5)^{3/2)}

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

- \frac{2}{( x - 5 ) ^{\frac{1}{2}}} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{\frac{3}{2}}} d u

= \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u ^{\frac{1}{2}}}

= - \frac{2}{u ^{\frac{1}{2}}}

Substitute back

u = x - 5

= - \frac{2}{( x - 5 ) ^{\frac{1}{2}}}

Add a constant to the solution

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

\frac{d}{d x} (\frac{( 3 x - 2 ) ( 2 x - 3 )}{- 2 x ^{2} + 4 x})

x y^{^{'}} + (1 + 2 x) y = 10 e^{- 2 x}

x \to + 1 lim (+ (\frac{1}{x ^{2} - 1}))

\int_{0}^{6} \frac{1}{36 + x ^{2}} d x

\frac{x}{( 2 x + 3 ) ^{3}}

What is the integral of 1/((x-5)^{3/2)} ?
The integral of 1/((x-5)^{3/2)} is -2/((x-5)^{1/2)}+C