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

Problem

(∫_^)(4*e(4*x)*d(x))

Solution

1. Identify the constant multiple rule for integration, which allows the constant 4 to be moved outside the integral.

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

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

(∫_^)(e(4*x)*d(x))=1/4*e(4*x)+C

3. Multiply the result by the constant 4 that was moved outside earlier.

4⋅1/4*e(4*x)+C

4. Simplify the expression by canceling the 4 in the numerator and denominator.

e(4*x)+C

Final Answer

(∫_^)(4*e(4*x)*d(x))=e(4*x)+C

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