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

Problem

(∫_^)(e^(5*x)*d(x))

Solution

1. Identify the form of the integral, which is the exponential function e^(a*x) where a=5

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

3. Substitute the value a=5 into the formula.

4. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(e^(5*x)*d(x))=(e^(5*x))/5+C

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