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Evaluate: int(x^2)/((x-1)(x-2)(x-3))\ dx...

Evaluate: `int(x^2)/((x-1)(x-2)(x-3))\ dx`

Text Solution

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`=frac{A}{x-1}+frac{B}{x-2}+frac{C}{x-3} ldots ldots(i) `

`Rightarrow frac{x^{2}}{(x-1)(x-2)(x-3)}`

`=frac{A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)}{(x-1)(x-2)(x-3)} `

`Rightarrow x^{2}=A(x-2)(x-3)+B(x-1)(x-3)

+C(x-1)(x-2) ldots ldots(text { ii })`

We need to solve for `A, B` and `C`.

One way to do this is to pick values for `x` which will cancel each variable.

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