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

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To integrate ( \frac{2x + 1}{(x - 2)(x^2 + 1)} ) using partial fractions, we first express the fraction as a sum of simpler fractions with unknown constants:

[ \frac{2x + 1}{(x - 2)(x^2 + 1)} = \frac{A}{x - 2} + \frac{Bx + C}{x^2 + 1} ]

Then, we find the values of ( A ), ( B ), and ( C ) by multiplying both sides by the denominator and equating the numerators:

[ 2x + 1 = A(x^2 + 1) + (Bx + C)(x - 2) ]

By expanding and comparing coefficients, we can solve for ( A ), ( B ), and ( C ). After finding their values, we substitute them back into the partial fraction decomposition and integrate each term separately. Finally, we combine the integrals to obtain the result.

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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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