What is the integral of (x^2)/((x-1)^{10)} ?

The integral of (x^2)/((x-1)^{10)} is -(x^2)/(9(x-1)^9)+(-8x+1)/(252(x-1)^8)+C

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integral of (x^2)/((x-1)^{10)}

\int \frac{x ^{2}}{( x - 1 ) ^{10}} d x

- \frac{x ^{2}}{9 ( x - 1 ) ^{9}} + \frac{- 8 x + 1}{252 ( x - 1 ) ^{8}} + C

Solution steps

\int \frac{x ^{2}}{( x - 1 ) ^{10}} d x

Apply Integration By Parts

= - \frac{x ^{2}}{9 ( x - 1 ) ^{9}} - \int - \frac{2 x}{9 ( x - 1 ) ^{9}} d x

\int - \frac{2 x}{9 ( x - 1 ) ^{9}} d x = - \frac{- 8 x + 1}{252 ( x - 1 ) ^{8}}

= - \frac{x ^{2}}{9 ( x - 1 ) ^{9}} - (- \frac{- 8 x + 1}{252 ( x - 1 ) ^{8}})

Simplify

= - \frac{x ^{2}}{9 ( x - 1 ) ^{9}} + \frac{- 8 x + 1}{252 ( x - 1 ) ^{8}}

Add a constant to the solution

= - \frac{x ^{2}}{9 ( x - 1 ) ^{9}} + \frac{- 8 x + 1}{252 ( x - 1 ) ^{8}} + C

What is the integral of (x^2)/((x-1)^{10)} ?
The integral of (x^2)/((x-1)^{10)} is -(x^2)/(9(x-1)^9)+(-8x+1)/(252(x-1)^8)+C