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

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2001-10-29