How to integrate -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt

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SUMMARY

The discussion focuses on the integration of the expression -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt, relevant for solving partial differential equations (PDEs). A user sought clarification on the solution provided by Wolfram Alpha, which was confirmed to be correct. The key takeaway is the application of the product rule for differentiation, which aids in deriving the integrand and subsequently solving the integral.

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  • Understanding of partial differential equations (PDEs)
  • Familiarity with integration techniques in calculus
  • Knowledge of differentiation, specifically the product rule
  • Experience using computational tools like Wolfram Alpha
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  • Study the application of the product rule in calculus
  • Explore integration techniques for complex functions
  • Learn about solving partial differential equations (PDEs) using various methods
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Students preparing for exams in calculus and partial differential equations, educators teaching advanced calculus concepts, and anyone seeking to enhance their integration skills.

lamba89
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Apply the product rule for differentiation to the solution. This gives you the integrand. If you recognize this then you just need to do the reverse to get the solution.
 
Thanks, I just realized it too
 

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