72. (a) Use integration by parts to show that, for any positive integer n, dx (x² + a²)" dx 2a (n - 1)(x² + a²)«-1 2n - 3 dx 2a (n – 1) (x² + a²)«-T (b) Use part (a) to evaluate dx dx and (x² + 1)² (x² + 1)
72. (a) Use integration by parts to show that, for any positive integer n, dx (x² + a²)" dx 2a (n - 1)(x² + a²)«-1 2n - 3 dx 2a (n – 1) (x² + a²)«-T (b) Use part (a) to evaluate dx dx and (x² + 1)² (x² + 1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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72. (a) Use integration by parts to show that, for any positive
x*(1- x)*
dx
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1 + x2
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na
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integer n,
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dx
dx
2a (n - 1)(x² + a²)•-1
2n - 3
dx
+
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(b) Use part (a) to evaluate
dx
dx
and
(x² + 1)²
(x² + 1)
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