Find the Integral e^(-x^2)

Problem

(∫_^)(e(−x2)*d(x))

Solution

1. Identify the integral as the Gaussian integral, which does not have an antiderivative expressible in terms of elementary functions.

2. Recall the definition of the error function, denoted as erf(x) which is used to express the antiderivative of e(−x2)

3. Apply the formula for the error function, which is defined as erf(x)=2/√(,π)*(∫_0^x)(e(−t2)*d(t))

4. Rearrange the relationship to solve for the indefinite integral of e(−x2)

5. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(e(−x2)*d(x))=√(,π)/2*erf(x)+C

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