Find the Antiderivative 2e^x

Problem

(∫_^)(2*ex*d(x))

Solution

1. Identify the constant multiple rule for integration, which allows the constant 2 to be moved outside the integral.

(∫_^)(2*ex*d(x))=2*(∫_^)(ex*d(x))

2. Apply the exponential integration rule, which states that the antiderivative of ex is ex

2*(∫_^)(ex*d(x))=2*ex+C

3. Include the constant of integration C to represent the family of all possible antiderivatives.

2*ex+C

Final Answer

(∫_^)(2*ex*d(x))=2*ex+C

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