Find the Antiderivative e^(x/2)

Problem

(∫_^)(e(x/2)*d(x))

Solution

1. Identify the form of the integral, which is an exponential function with a linear exponent of the form e(a*x)

2. Apply the rule for the antiderivative of e(a*x) which states that (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

3. Determine the constant a by looking at the exponent x/2 which means a=1/2

4. Substitute the value of a into the formula to get 1/(1/2)*e(x/2)+C

5. Simplify the coefficient by calculating the reciprocal of 1/2 which is 2

Final Answer

(∫_^)(e(x/2)*d(x))=2*e(x/2)+C

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