What is the integral of 1/((x-a)^n) ?

The integral of 1/((x-a)^n) is ((-a+x)^{-n+1})/(-n+1)+C

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integral of 1/((x-a)^n)

\int \frac{1}{( x - a ) ^{n}} d x

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

Solution steps

\int \frac{1}{( x - a ) ^{n}} d x

Apply u-substitution

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

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

Apply the Power Rule

: \frac{u ^{- n + 1}}{- n + 1}

= \frac{u ^{- n + 1}}{- n + 1}

Substitute back

u = - a + x

= \frac{( - a + x ) ^{- n + 1}}{- n + 1}

Add a constant to the solution

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

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