Find the Antiderivative sin(3x)

Problem

(∫_^)(sin(3*x)*d(x))

Solution

1. Identify the form of the integral, which is a trigonometric function with a linear argument a*x+b

2. Apply the rule for the antiderivative of sin(a*x) which is −1/a*cos(a*x)+C

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

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

Final Answer

(∫_^)(sin(3*x)*d(x))=−1/3*cos(3*x)+C

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