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

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0x2m+1sin(ax)(z+x2)n+1?dx=(1)n+mn!π2dndzn(zmeaz)[a >0,0mn,|argz|< π]

si3086_e  ET I 68(39)

3.12 

0x2m+1sin(ax)dx(b2+x2)n+12?=(1)m+1πd2m+12nbnΓ(n+12)da2m+1[anKn(ab)]

si3087_e  ET I 67(37)

[a >0,Reb>0,1m<n]si3088_e

4. 

0x2νcos(ax)dx(x2+b2)μ+1=12b2ν2μ1B(ν+12,μν+12)F12(ν+12;νμ+12,12;b2a24)+πa2μ2ν+14μν+1Γ(νμ12)Γ(μν+12)F12(μ+1;μν+1,μν+32;b2a24=π2Γ(μ+1)b2ν2μ1?G1321(a2b24|μν+12,0,12ν+12)

  ET I 14(29)a, ET II 235(19)

[a >0,Reb>0,12<Rev<Reμ+1]

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