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

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

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

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

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

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

Add a constant to the solution

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

f (x) = x^{9} ln (4 x)

\frac{d}{d x} (1. 8^{0.045 x} - 1)

\int \frac{y ^{2} + 2 y + 1}{y} d y

\frac{4 x}{x + 3} (1.1)

n = 0 \sum \infty e^{- 4 n}

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