Evaluate the Integral integral of 2e^x with respect to x

Problem

(∫_^)(2*ex*d(x))

Solution

1. Identify the constant factor in the integrand.

2. Apply the constant multiple rule for integration by moving the constant 2 outside the integral sign.

(∫_^)(2*ex*d(x))=2*(∫_^)(ex*d(x))

3. Apply the exponential rule for integration, which states that (∫_^)(ex*d(x))=ex+C

2*(∫_^)(ex*d(x))=2*(ex+C)

4. Simplify the expression by distributing the constant, noting that 2 times an arbitrary constant C is still an arbitrary constant C

2*ex+C

Final Answer

(∫_^)(2*ex*d(x))=2*ex+C

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