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

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

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integral of 1/((x-2)^3)

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

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

Solution steps

\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

\int x^{3} (x^{4} + 16)^{4} d x

\frac{d}{d x} (- cot (x) csc (x))

x \to 5 lim (2 x^{2} - 3 x + 7)

f (x) = 1 + cos (x)

\frac{x d x + y d y}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}} = 0

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