Evaluate the Integral integral of 2e^(5x) with respect to x

Problem

(∫_^)(2*e(5*x)*d(x))

Solution

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

(∫_^)(2*e(5*x)*d(x))=2*(∫_^)(e(5*x)*d(x))

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

2*(∫_^)(e(5*x)*d(x))=2*(1/5*e(5*x))+C

3. Simplify the expression by multiplying the constants.

2*(1/5*e(5*x))+C=2/5*e(5*x)+C

Final Answer

(∫_^)(2*e(5*x)*d(x))=2/5*e(5*x)+C

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