Find the indicated series by the given operation. Show that by integrating term by term the expansion of - 2х the result is the expansion for In (1- x2). 1- x2 S(-2x+ 2x3 - 25 + 2x7-.) 1 -...) dx = -x2 += x4 xb S(2x- 2x3. 25 - 2x7..) dx = x² . =x2 . 2 1 + 1 .. S(-2x- 2x3 - 2x5 – 2x7 -...) dx = -x² . x4 1.6 1 S2x+ 23 . 2x5 + 2x7..) dx = x² + (2x + 2x3 + 2x5 + 2x7. +...) dx 1 1 x4 + XO +. . .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the indicated series by the given operation.
Show that by integrating term by term the expansion of -
2x
the result is the expansion for In (1 - x2).
1- x2
1
S(-2x+ 2x3- 25+ 2x7 - .. ) da " x2 .
(-2x +
-..) dx = -x2 +
x4
X° +
Sex- 23. 25 - 2x7..) e x2
(2x- 2x3 + 2x5 - 2x7..) dx
2
1
1
x4
+
w/
..
1
S = x2.
(-2x- 2x3 - 2x5 - 2x7 - ...) dx
x4
S2x+ 2x3+ 25 + 2x7...) dx = x² +
(2x + 2x + 2x5 + 2x7 +...) dx
1
x4
3
+
X° +...
Transcribed Image Text:Find the indicated series by the given operation. Show that by integrating term by term the expansion of - 2x the result is the expansion for In (1 - x2). 1- x2 1 S(-2x+ 2x3- 25+ 2x7 - .. ) da " x2 . (-2x + -..) dx = -x2 + x4 X° + Sex- 23. 25 - 2x7..) e x2 (2x- 2x3 + 2x5 - 2x7..) dx 2 1 1 x4 + w/ .. 1 S = x2. (-2x- 2x3 - 2x5 - 2x7 - ...) dx x4 S2x+ 2x3+ 25 + 2x7...) dx = x² + (2x + 2x + 2x5 + 2x7 +...) dx 1 x4 3 + X° +...
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