Find the Antiderivative e^(x^2)

Problem

(∫_^)(e^(x^2)*d(x))

Solution

1. Identify the integral as one that cannot be expressed in terms of elementary functions (such as polynomials, logarithms, or trigonometric functions).

2. Recognize that the antiderivative of e^(x^2) is defined using the imaginary error function, denoted as erfi(x)

3. Apply the definition of the imaginary error function, which is related to the standard error function erf(x) by the relation erfi(x)=−i*erf*(i*x)

4. State the result using the standard form for this non-elementary integral, which includes the constant of integration C

Final Answer

(∫_^)(e^(x^2)*d(x))=√(,π)/2*erfi(x)+C

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