# How do you integrate #int (x^3-x^2+1) / (x^4-x^3)# using partial fractions?

The answer is

Divide the breakdown into partial fractions.

Compare the numerators; the denominators are the same.

Consequently,

So,

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To integrate the given rational function using partial fractions, you first decompose it into simpler fractions. The partial fraction decomposition for (\frac{{x^3 - x^2 + 1}}{{x^4 - x^3}}) is:

(\frac{{x^3 - x^2 + 1}}{{x^4 - x^3}} = \frac{{A}}{{x}} + \frac{{B}}{{x^2}} + \frac{{C}}{{x - 1}} + \frac{{D}}{{x^2 - 1}})

After finding the values of A, B, C, and D, you can integrate each term separately. The solution involves finding the values of A, B, C, and D by equating coefficients and then integrating each term individually.

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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.

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.

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.

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