2. (a) Express f(x) = %3D (x² + 1)² into partial fractions. Hence, using the substitution x = tan0 or otherwise, prove that f (x)dx (п — 2). 8. EPARI

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.10: Partial Fractions
Problem 12E
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Solve detailly 2a, b

x2
2. (a) Express f (x)
into partial fractions.
%3D
(x2 + 1)2
Hence, using the substitution x = tan0 or otherwise, prove that
1
f (x)dx
(-2).
8.
(b) Given that In = ||
(Inx)" dx, show that
%3D
-nln- 1
Hence, evaluate I3.
ND THE PREPARI
Transcribed Image Text:x2 2. (a) Express f (x) into partial fractions. %3D (x2 + 1)2 Hence, using the substitution x = tan0 or otherwise, prove that 1 f (x)dx (-2). 8. (b) Given that In = || (Inx)" dx, show that %3D -nln- 1 Hence, evaluate I3. ND THE PREPARI
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