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

Problem

(∫_^)(8*e(4*y)*d(y))

Solution

1. Identify the constant and the form of the integral, which follows the rule (∫_^)(e(a*y)*d(y))=1/a*e(a*y)+C

2. Factor out the constant 8 from the integral to simplify the expression.

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

3. Apply the rule for integrating an exponential function e(a*y) where a=4

8*(∫_^)(e(4*y)*d(y))=8⋅(e(4*y))/4+C

4. Simplify the expression by dividing the coefficients.

8⋅(e(4*y))/4+C=2*e(4*y)+C

Final Answer

(∫_^)(8*e(4*y)*d(y))=2*e(4*y)+C

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