Find the Integral 2e^(2x)

Problem

(∫_^)(2*e^(2*x)*d(x))

Solution

1. Identify the constant and the form of the integral, noting that the constant 2 can be moved outside the integral sign.

(∫_^)(2*e^(2*x)*d(x))=2*(∫_^)(e^(2*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

2*(∫_^)(e^(2*x)*d(x))=2⋅1/2*e^(2*x)+C

3. Simplify the expression by multiplying the constants.

2⋅1/2=1

Final Answer

(∫_^)(2*e^(2*x)*d(x))=e^(2*x)+C

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