If yields ao ln x + a₁ ln x + 1| + + an ln |x +n + c where ai (i = 0, 1,,n) and c are real constants, find an (a) (b) (c) 1-77 n! dx √ x(x + 1)(x + n) 1 n! (-1)n+1 1 n! (d) (e) (-1)n-¹ n!

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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Please find the solution of the problem in the uploaded photo.

If
dx
J r(x+1) .· (x + n)
yields
ao In |æ| + a1 ln |x + 1| + ... + an In |x + n| +c
where a; (i = 0, 1, · · · , n) and c are real constants, find
an-
(a)
n!
(b) п!
1
(c)
n!
1
(d) (-1)"+1 -
n!
(e) (-1)"
n!
Transcribed Image Text:If dx J r(x+1) .· (x + n) yields ao In |æ| + a1 ln |x + 1| + ... + an In |x + n| +c where a; (i = 0, 1, · · · , n) and c are real constants, find an- (a) n! (b) п! 1 (c) n! 1 (d) (-1)"+1 - n! (e) (-1)" n!
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