Evaluate the Integral integral of 3e^x with respect to x

Problem

(∫_^)(3*ex*d(x))

Solution

1. Identify the constant multiple in the integrand.

2. Apply the constant multiple rule for integration, which allows moving the constant 3 outside the integral sign.

(∫_^)(3*ex*d(x))=3*(∫_^)(ex*d(x))

3. Apply the basic integration rule for the natural exponential function, where (∫_^)(ex*d(x))=ex+C

3*(∫_^)(ex*d(x))=3*(ex+C)

4. Simplify the expression by distributing the constant, noting that 3 times an arbitrary constant C is still an arbitrary constant C

3*ex+C

Final Answer

(∫_^)(3*ex*d(x))=3*ex+C

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