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

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

Text Solution

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

`Rightarrow int frac{x^{3}}{x^{2}-3 x+2} d x `

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

`Rightarrow int 1 d x+int frac{3 x-2}{(x-1)(x-2)} d x`

This can be written as

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