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Partial Fraction 2 Notes

# Partial Fraction 2 Notes - Example 0.1 Z x 3 x 2 2 dx...

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Partial Fractions 2 (Section 7.4) Integrating Z p ( x ) q ( x ) : If the degree of p ( x ) is greater than the degree of q ( x ), start by using polynomial long division. Then use the method of partial fractions on the remainder. Rule 1: If the denominator of p ( x ) q ( x ) is the product of linear factors, none of which are repeated, that is, q ( x ) = ( a 1 x + b 1 )( a 2 x + b 2 ) ... ( a n x + b n ), then p ( x ) q ( x ) = A 1 a 1 x + b 1 + A 2 a 2 xb 2 + ... + A n a n x + b n Rule 2: If the denominator is the product of linear factors, some of which are repeated, the repeated factor ( ax + b ) r contributes A 1 ax + b + A 2 ( ax + b ) 2 + A 3 ( ax + b ) 3 + ... + A r ( ax + b ) r The remaining factors contribute terms using the appropriate rules.

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Unformatted text preview: Example 0.1. Z x + 3 ( x + 2) 2 dx Example 0.2. Z x 2 ( x-1)( x 2 + 2 x + 1) dx Rule 3: If the denominator has an irreducible quadratic factor ax 2 + bx + c , the quadratic factor contributes a term Ax + B ax 2 + bx + c to the partial fractions decomposition of p ( x ) q ( x ) . Example 0.3. Z 2 x 2-x + 4 x 3 + 4 x dx Example 0.4. Z 2 s + 2 ( s 2 + 1)( s-1) 2 ds Example 0.5. Determine the coeﬃcient on the ln( x 2 + 1) term in the evaluated integral Z 2 x-4 x 3 + x dx ....
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Partial Fraction 2 Notes - Example 0.1 Z x 3 x 2 2 dx...

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