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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = x - 2

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (2)

\frac{d}{d x} ((x y)^{\frac{1}{2}})

x \to 0 lim (\frac{tan ( x )}{6 x})

- 5 cos (5 t)

x y \frac{d y}{d x} = x^{2} - y^{2}

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