Evaluate the Integral integral of 8e^(4x) with respect to x

Problem

(∫_^)(8*e(4*x)*d(x))

Solution

1. Identify the constant and move it outside the integral to simplify the expression.

(∫_^)(8*e(4*x)*d(x))=8*(∫_^)(e(4*x)*d(x))

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

8*(∫_^)(e(4*x)*d(x))=8⋅1/4*e(4*x)+C

3. Simplify the resulting expression by multiplying the constants.

8⋅1/4*e(4*x)+C=2*e(4*x)+C

Final Answer

(∫_^)(8*e(4*x)*d(x))=2*e(4*x)+C

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