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2°) Use integration by parts to prove that, for any positive integer n, (2n + 1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n. (n!)2 In (2n + 1)!"

2°) Use integration by parts to prove that, for any positive integer n, (2n + 1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n. (n!)2 In (2n + 1)!"

Advanced Engineering Mathematics
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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i really just need help with 2 and 3

Let In = | (1- t2)" dt, for any nonnegative integer n. 1°) Calculate Io and I1. 2°) Use integration by parts to prove that, for any positive integer n, (2n +1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n . (n!)2 In (2n + 1)! %3D
Transcribed Image Text:Let In = | (1- t2)" dt, for any nonnegative integer n. 1°) Calculate Io and I1. 2°) Use integration by parts to prove that, for any positive integer n, (2n +1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n . (n!)2 In (2n + 1)! %3D
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