Finding the integral of an improper fraction

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    Fraction Integral
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SUMMARY

The integral of the improper fraction (12x² + x - 12)/(3x - 2) can be simplified using long division, resulting in 4x - 3 with a remainder of -6. This means the integral can be expressed as the sum of the integral of (4x - 3) and the integral of -6/(3x - 2). The correct approach to solving this integral involves performing the integration of both components separately.

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Homework Statement



Use substitution to find the integral of (12x2 + X -12)/(3x - 2)


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The Attempt at a Solution



I know I need to use long division to work it down to a proper fraction. That is where my real problem lies. Using long division I get that (12x2+x-12)/(3x-2) is equal to 4x-3 with a remainder of -6. I don't really understand what that means in terms of my question, especially with the remainder. Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?
 
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howsockgothap said:
Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?

Yes, assuming that your long division is correct. You should know how to take the integral of (4x-3) - 6/(3x-2).
 
right on, thanks.
 

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