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

thus it is possible for us to state that

Since B*3 = 3 and x = 1, B = 1.

Since A*(-3) = 3 when x = -2, A = -1.

Consequently, the integral becomes

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

- Factor the denominator ( x^2 + x - 2 ) into ( (x + 2)(x - 1) ).
- Write the original expression as a sum of two fractions with unknown numerators, over each of the factors: ( \frac{A}{x + 2} + \frac{B}{x - 1} ).
- Clear the denominators by multiplying both sides by ( (x + 2)(x - 1) ).
- Simplify and equate coefficients to find the values of ( A ) and ( B ).
- Once you have found ( A ) and ( B ), rewrite the original expression using the partial fractions.
- Integrate each partial fraction separately.
- Finally, add the results of the integrations together to get the final solution.

The integration of each partial fraction ( \frac{A}{x + 2} ) and ( \frac{B}{x - 1} ) can be done using standard integration techniques, such as logarithmic substitution or direct integration.

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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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