Evaluate the Integral integral of 4e^(2x) with respect to x

Problem

(∫_^)(4*e(2*x)*d(x))

Solution

1. Identify the constant and move it outside the integral sign.

(∫_^)(4*e(2*x)*d(x))=4*(∫_^)(e(2*x)*d(x))

2. Apply the rule for integrating exponential functions of the form e(a*x) which is (∫_^)(e(a*x)*d(x))=1/a*e(a*x)+C

4*(∫_^)(e(2*x)*d(x))=4⋅1/2*e(2*x)+C

3. Simplify the expression by multiplying the constants.

4⋅1/2*e(2*x)+C=2*e(2*x)+C

Final Answer

(∫_^)(4*e(2*x)*d(x))=2*e(2*x)+C

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