How do you integrate #int 2/((1x)(1+x^2)) dx# using partial fractions?
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To integrate ( \frac{2}{(1x)(1+x^2)} ) using partial fractions, first express the fraction in the form of partial fractions, then integrate each term separately. The steps are as follows:

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

Multiply both sides by ( (1x)(1+x^2) ) to clear the denominators.

Equate the numerators to find the values of ( A ), ( B ), and ( C ).

Once you've found the values of ( A ), ( B ), and ( C ), integrate each term separately.

The final integral will be the sum of the integrals of each term.
After integrating each term, you'll have your 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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