How do you integrate #int (3x4)/((x1)(x+3)(x+4)) # using partial fractions?
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To integrate (\frac{{3x  4}}{{(x  1)(x + 3)(x + 4)}}) using partial fractions, you need to first express it as a sum of simpler fractions. The steps are as follows:

Decompose the given fraction into partial fractions: (\frac{{3x  4}}{{(x  1)(x + 3)(x + 4)}} = \frac{A}{x  1} + \frac{B}{x + 3} + \frac{C}{x + 4})

Multiply both sides by the common denominator ((x  1)(x + 3)(x + 4)): (3x  4 = A(x + 3)(x + 4) + B(x  1)(x + 4) + C(x  1)(x + 3))

Solve for (A), (B), and (C) by equating coefficients of like terms.

Once you find the values of (A), (B), and (C), substitute them back into the partial fraction decomposition.

Now, integrate each term separately.
After integration, you will obtain the final result.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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