Fresnel integral C: Integration (formula 06.33.21.0106)

FresnelC

$Mathematica Notation$

Gamma, Beta, Erf

FresnelC[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving logarithm and a power function

Involving log and power

Linear arguments

http://functions.wolfram.com/06.33.21.0106.01

Input Form

Integrate[z^2 Log[b z] FresnelC[a z], z] == (1/(18 a^3 Pi^2)) ((-1 + I a^2 Pi z^2 + E^(I a^2 Pi z^2) (-1 - I a^2 Pi z^2) + 3 E^((1/2) I a^2 Pi z^2) (ExpIntegralEi[(-(1/2)) I a^2 Pi z^2] + ExpIntegralEi[ (1/2) I a^2 Pi z^2]) + 3 I (2 I - a^2 Pi z^2 + E^(I a^2 Pi z^2) (2 I + a^2 Pi z^2)) Log[b z] + 2 a^3 E^((1/2) I a^2 Pi z^2) Pi^2 z^3 FresnelC[a z] (-1 + 3 Log[b z]))/ E^((1/2) I a^2 Pi z^2))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29