Integrate[z^2 CosIntegral[b z] SinhIntegral[a z], z] == (1/6) ((1/b^3) (I (-ExpIntegralEi[(a - I b) z] + ExpIntegralEi[(-(a + I b)) z] + ExpIntegralEi[(a + I b) z] - ExpIntegralEi[(-a) z + I b z])) + (1/(2 b^2)) (I ((2 E^((a - I b) z))/(I a + b) + 2/(E^((a + I b) z) (I a - b)) + (2 E^((a + I b) z))/(I a - b) + (2 E^((-a) z + I b z))/(I a + b) + (b Gamma[2, (a - I b) z])/ (I a + b)^2 - (b Gamma[2, (-(a + I b)) z])/((-I) a + b)^2 - (b Gamma[2, (a + I b) z])/((-I) a + b)^2 + (b Gamma[2, (-a) z + I b z])/ (I a + b)^2)) - (1/(2 a^3)) (-((a E^((a - I b) z) (2 I b + a^2 z + a (-3 - I b z)))/(a - I b)^2) + (a E^((-a) z + I b z) (-2 I b + a^2 z + a (3 - I b z)))/(a - I b)^2 - (a E^((a + I b) z) (-2 I b + a^2 z + a (-3 + I b z)))/(a + I b)^2 + (a (2 I b + a^2 z + a (3 + I b z)))/(E^((a + I b) z) (a + I b)^2) - 2 ExpIntegralEi[(a - I b) z] - 2 ExpIntegralEi[(-(a + I b)) z] - 2 ExpIntegralEi[(a + I b) z] - 2 ExpIntegralEi[(-a) z + I b z] + 2 CosIntegral[b z] (Gamma[3, (-a) z] + Gamma[3, a z])) + 2 z^3 CosIntegral[b z] SinhIntegral[a z] - (1/b^3) (I (Gamma[3, (-I) b z] - Gamma[3, I b z]) SinhIntegral[a z]))

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> z </ci> </apply> 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</cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29