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Integrate ex2e^{-x^2}

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Q. Integrate ex2e^{-x^2}
  1. Use Special Function: Step Title: Use a Special Function\newlineCalculation: Acknowledge that the antiderivative of e(x2)e^{(-x^2)} involves the error function, denoted as erf(x)\text{erf}(x).
  2. Write Integral in Terms: Step Title: Write the Integral in Terms of erf(x)\text{erf}(x)\newlineCalculation: The integral of ex2e^{-x^2} dx is (π/2)×erf(x)\left(\sqrt{\pi}/2\right) \times \text{erf}(x).