anonymous
  • anonymous
Super hard calculus problem! Can you help? The closed form solution of the integral of e^(x^2)dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
There is no closed form solution, however the integral of e^(x^2) can easily be found using the maclaurin expansion for e^u. e^u = 1+ u +u^2/2! + u^3/3! + u^4 /4! +.... let u=x^2 e^(x^2) = 1 + x^2 + x^4/2! + x^6/3! + x^8/ 4!+..... Then integral of e^(x^2)dx is x + x^3/ 3 + x^5/(5*2!) + x^7/(7*3!) + x^9/(9*4!) + ...... + C That is its exact antiderivitive (and not an approximation). No 'closed form' antiderivitive means its antiderivitive cannot be expressed as a sum,product,difference, or quotient of a finite number of elementary functions. Elementary functions are typically considered to be the trigonometric, inverse trigonometric, exponential, logarithmic, and algebraic functions.
tkhunny
  • tkhunny
Nothing hard about it. It can't be done. Look up "erf(x)" or the Error Function. There is plenty of literature on it.

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