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Question Number 67942 by mhmd last updated on 02/Sep/19

∫e^(y^2 /2)   dy

$$\int{e}^{{y}^{\mathrm{2}} /\mathrm{2}} \:\:{dy} \\ $$

Commented by mr W last updated on 09/Feb/21

∫e^(y^2 /2) dy=(√(π/2)) erfi((y/( (√2))))+C  ∫e^(−(y^2 /2)) dy=(√(π/2)) erf((y/( (√2))))+C  erf(), erfi() = error functions

$$\int{e}^{\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erfi}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C} \\ $$$$\int{e}^{−\frac{{y}^{\mathrm{2}} }{\mathrm{2}}} {dy}=\sqrt{\frac{\pi}{\mathrm{2}}}\:{erf}\left(\frac{{y}}{\:\sqrt{\mathrm{2}}}\right)+{C} \\ $$$${erf}\left(\right),\:{erfi}\left(\right)\:=\:{error}\:{functions} \\ $$

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