Evaluate the Integral integral of 5^x with respect to x

Problem

(∫_^)(5*d(x))

Solution

1. Identify the form of the integral as an exponential function ax where a=5

2. Apply the formula for the integral of an exponential function, which states (∫_^)(ax*d(x))=(ax)/ln(a)+C for any positive constant a≠1

3. Substitute a=5 into the formula to find the antiderivative.

4. Add the constant of integration C to represent the family of all possible antiderivatives.

Final Answer

(∫_^)(5*d(x))=5/ln(5)+C

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