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1. Evaluate the given using Integration by Partial Fractions (pls follow the format on the reference: A and B as variables) -6x + 10 dx J p²(x² + 2x + 5)

1. Evaluate the given using Integration by Partial Fractions (pls follow the format on the reference: A and B as variables) -6x + 10 dx J p²(x² + 2x + 5)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.6: Partial Fractions
Problem 61E
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Apply integration by partial fractions (where x is related to A, B, C). I provided reference on the 2nd photo. pls skip if unsure & not willing to answer completely. Thanks!

1. Evaluate the given using Integration by Partial Fractions (pls follow the format on the reference: A and B as variables) -6x + 10 dx x² (x² + 2x + 5)
Transcribed Image Text:1. Evaluate the given using Integration by Partial Fractions (pls follow the format on the reference: A and B as variables) -6x + 10 dx x² (x² + 2x + 5)
Kindly use this reference to provide complete solutions for 1: Case 1: Denominator has distinct linear factors If g(x) = (a)x+ bị)(a2x+ b2).…· (a,x+ b,), where all factors are distinct, then f(x) g(x) a1x+ bj ' azx+b2 A A2 A, anx+ b,' for some real numbers Aj,...,A,. Case 2: Denominator has repeated linear factors If (ax+ b)", n> 1, is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A A2 ax+ b' (ax+ b)² A, (ax+ b)"' for some real numbers Aj,..,An. Case 3: Denominator has an irreducible quadratic factor If ax + bx+ c, a+0, is an irreducible quadratic factor of the denominator that is not repeated , then the corresponding partial fraction is of the form Ax+ B ax² + bx+ c' for some real numbers Aand B. If (ax? + bx + c)", n>1 is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A1x+ B1 ax² + bx + c ° (ax² + bx+ c)² Azx+ B2 Anx+ Bn (ax² + bx+ c)" for some real numbers Aj..An, B1..,Bp. If ax + bx+ c, a#0, is an irreducible quadratic factor of the denominator that is not repeated, then the corresponding partial fraction is of the form Ax+ B ax² + bx+ c' for some real numbers A and B. If (ax? + bx + c)", n >1 is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A1x+ BỊ ax² + bx+ c' (ax + bx+ c)² for some real numbers Aj,..,A, B1,..,Bp- A2x + B2 Anx + Bn +...+ (ax² + bx + c)"
Transcribed Image Text:Kindly use this reference to provide complete solutions for 1: Case 1: Denominator has distinct linear factors If g(x) = (a)x+ bị)(a2x+ b2).…· (a,x+ b,), where all factors are distinct, then f(x) g(x) a1x+ bj ' azx+b2 A A2 A, anx+ b,' for some real numbers Aj,...,A,. Case 2: Denominator has repeated linear factors If (ax+ b)", n> 1, is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A A2 ax+ b' (ax+ b)² A, (ax+ b)"' for some real numbers Aj,..,An. Case 3: Denominator has an irreducible quadratic factor If ax + bx+ c, a+0, is an irreducible quadratic factor of the denominator that is not repeated , then the corresponding partial fraction is of the form Ax+ B ax² + bx+ c' for some real numbers Aand B. If (ax? + bx + c)", n>1 is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A1x+ B1 ax² + bx + c ° (ax² + bx+ c)² Azx+ B2 Anx+ Bn (ax² + bx+ c)" for some real numbers Aj..An, B1..,Bp. If ax + bx+ c, a#0, is an irreducible quadratic factor of the denominator that is not repeated, then the corresponding partial fraction is of the form Ax+ B ax² + bx+ c' for some real numbers A and B. If (ax? + bx + c)", n >1 is a factor of the denominator, then corresponding to this factor is the sum of n partial fractions A1x+ BỊ ax² + bx+ c' (ax + bx+ c)² for some real numbers Aj,..,A, B1,..,Bp- A2x + B2 Anx + Bn +...+ (ax² + bx + c)"
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