How do you find #int (7x^2+x1) / ((2x+1) (x^24x+4)) dx# using partial fractions?
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To find the integral of (\frac{7x^2+x1}{(2x+1)(x^24x+4)}) using partial fractions:

Factor the denominator ( (2x+1)(x^24x+4) ) into irreducible factors: ( (2x+1)(x2)^2 ).

Write the fraction in partial fraction form: ( \frac{A}{2x+1} + \frac{B}{x2} + \frac{C}{(x2)^2} ).

Multiply both sides of the equation by the denominator to clear the fractions.

Combine the terms and equate coefficients to find the values of ( A ), ( B ), and ( C ).

Integrate each term separately.

The integral of the original expression will be the sum of the integrals of the partial fractions.
Following these steps, you can solve the integral using partial fractions.
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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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