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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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xnsin x dx = xnn + k=1  (1)k + 12(22k  1  1)(n + 2k)(2k)!B2kxn + 2k[ |x| < π, n > 0]

si2057_e

TU (333)(8b)

4.12 

xnxnsinx dx =   1nxn    [ 1 + (  1)n]( 1)n22n - 1  1n!Bnln x  k=1kn2  (1)k 2(22n  1)(2k   n)(2k)!B2kx2k  n                                                                                                            [ n > 1,|x| < π,]

si2058_e

GU (333)(9b)

5.8 

xn dxcos x = k=0| E2k|xn + 2k + 1(n + 2k + 1)(2k)!                                             [ |x| < π2, n  > 0]

GU (333)(10b)

6. 

 dxxn cos x =  12[ 1 (1)n] 

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