Integrating e^(-bx²) times its second derivative

[clumps tim]

hi , i need some help in this integral

e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinityI tried differentiating e^(-bx^2) twice and it came up weird , is there any other way to do it ?

 

[Opalg]

hi , i need some help in this integral

e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinityI tried differentiating e^(-bx^2) twice and it came up weird , is there any other way to do it ?

Integration by parts looks like a promising first step.