Integrate[z E^(b z) Cos[c z] FresnelC[a z], z] == (-(1/(4 a^2 Pi))) ((1/(b - I c)^2) (-2 a^2 E^((b - I c) z) Pi (-1 + b z - I c z) FresnelC[a z] + E^((I (b - I c)^2)/(2 a^2 Pi)) ((b - I c)^2 + I a^2 Pi) (FresnelC[(b - I c)/(a Pi) + I a z] - I FresnelS[(b - I c)/(a Pi) + I a z]) + (((b - I c)^2 - I a^2 Pi) (FresnelC[(b - I (c + a^2 Pi z))/(a Pi)] - FresnelS[(I b + c)/(a Pi) + a z]))/E^((I (b - I c)^2)/(2 a^2 Pi)) + 2 a (b - I c) E^((b - I c) z) Sin[(1/2) a^2 Pi z^2]) + (1/(b + I c)^2) (-2 a^2 E^((b + I c) z) Pi (-1 + b z + I c z) FresnelC[a z] + (((b + I c)^2 - I a^2 Pi) (FresnelC[(b + I c)/(a Pi) - I a z] + I FresnelS[(b + I c)/(a Pi) - I a z]))/ E^((I (b + I c)^2)/(2 a^2 Pi)) + E^((I (b + I c)^2)/(2 a^2 Pi)) ((b + I c)^2 + I a^2 Pi) (FresnelC[(b + I c)/(a Pi) + I a z] - I FresnelS[(b + I c)/(a Pi) + I a z]) + 2 a (b + I c) E^((b + I c) z) Sin[(1/2) a^2 Pi z^2]))

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2001-10-29