# What is #int (x^3-2x^2+6x-3 ) / (-x^2+ 9 x +2 )#?

We have to simplify the third term, so that

the continuation is

Now, we are ready to integrate

also by "completing the square"

and

God bless....I hope the explanation is useful.

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The expression ( \frac{{x^3 - 2x^2 + 6x - 3}}{{-x^2 + 9x + 2}} ) can be simplified by polynomial division. The quotient is ( x + 7 ) with a remainder of ( \frac{{-57x + 1}}{{x^2 - 9x - 2}} ).

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