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integrate thisint ( x^2+1)/(x^2-5x+6)dx...

integrate this`int ( x^2+1)/(x^2-5x+6)dx`

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`int ( x^2+1)/(x^2-5x+6)dx`
`int ( x^2+1)/(x^2-5x+6)dx=int ( x^2+1-5x+6+5x-6)/(x^2-5x+6)dx ` (Adding and subtracting -5x+6) `=((x^2-5x+6)+(5x-5))/(x^2-5x+6)`
`=(x^2-5x+6)/(x^2-5x+6)+(5x-5)/(x^2-5x+6)`

`=1+(5x-5)/(x^2-5x+6)`

`=1+(5x-5)/(x(x-2)-3(x-2))`

`=1+(5x-5)/((x-2)(x-3))`

Now solving `(5x-5)/((x-2)(x-3))` using partial fractions

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