Find the Integral e^(x^2)

Problem

(∫_^)(e(x2)*d(x))

Solution

1. Identify the type of integral. The function e(x2) does not have an elementary antiderivative, meaning it cannot be expressed in terms of basic functions like polynomials, logarithms, or trigonometric functions.

2. Recognize the relationship to the error function. The integral is related to the imaginary error function, denoted as erfi(x) which is defined via the integral of e(t2)

3. Apply the definition of the imaginary error function. The standard definition is erfi(x)=2/√(,π)*(∫_0^x)(e(t2)*d(t))

4. Solve for the indefinite integral by rearranging the definition and adding the constant of integration C

Final Answer

(∫_^)(e(x2)*d(x))=√(,π)/2*erfi(x)+C

Want more problems? Check here!