Evaluate the Integral integral of 3e^(3x) with respect to x

Problem

(∫_^)(3*e(3*x)*d(x))

Solution

1. Identify the constant and the function to be integrated. The constant 3 can be moved outside the integral.

(∫_^)(3*e(3*x)*d(x))=3*(∫_^)(e(3*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

(∫_^)(e(3*x)*d(x))=1/3*e(3*x)+C

3. Multiply the result by the constant 3 that was moved outside.

3⋅1/3*e(3*x)+C

4. Simplify the expression by canceling the 3 in the numerator and denominator.

e(3*x)+C

Final Answer

(∫_^)(3*e(3*x)*d(x))=e(3*x)+C

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