Integral Calculus Help - Differentiating e^(-bx^2)

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SUMMARY

The discussion focuses on the integral of the function e^(-bx^2) and the challenges associated with differentiating it twice. The user encountered difficulties when attempting to differentiate e^(-bx^2) twice, leading to confusion about the results. A suggested solution is to utilize integration by parts as a viable method to approach this integral effectively.

PREREQUISITES
  • Understanding of integral calculus concepts
  • Familiarity with differentiation techniques
  • Knowledge of the exponential function and its properties
  • Experience with integration by parts method
NEXT STEPS
  • Research the integration by parts technique in detail
  • Study the properties of the Gaussian function e^(-bx^2)
  • Explore advanced differentiation techniques for exponential functions
  • Learn about the applications of e^(-bx^2) in probability and statistics
USEFUL FOR

Students and professionals in mathematics, particularly those studying calculus, as well as anyone seeking to deepen their understanding of integrals involving exponential functions.

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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 ?
 
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cooper607 said:
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.
 

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