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How do you integrate #f(x)=(3x^2-x)/((x^2-52)(x+4)(x-7))# using partial fractions?

Answer 1

Isabella Ackerman

See the answer below:

Credits: Thanks very much to the web site https://tutor.hix.ai who helped us with the "huge" system of equations.

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Answer 2

Evelyn Agard

To integrate ( f(x) = \frac{{3x^2 - x}}{{(x^2 - 52)(x + 4)(x - 7)}} ) using partial fractions, follow these steps:

Factor the denominator ( (x^2 - 52)(x + 4)(x - 7) ).
Write ( f(x) ) as a sum of partial fractions.
Solve for the constants in the partial fraction decomposition.
Integrate each partial fraction separately.
Combine the integrals to get the final result.

The detailed solution involves algebraic manipulations and solving for the constants in the partial fraction decomposition. If you need assistance with the step-by-step process or further clarification on any specific step, feel free to ask.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.