In other word how can I prove that its integration is 1?

 

here is the problem

 

If you can do the integration, you do it or look in Abramowitz and Stegun, Handbook of Mathematical Functions, Dover, 1972, pp. 255-293
If there is no closed form for the indefinite integral, you may have to rely on a numerical integration.

https://www.amazon.com/Handbook-Mat...9535957&sr=8-1&keywords=Abramowitz+and+Stegun