Find the Antiderivative f(x)=sin(2x)

Problem

(∫_^)(sin(2*x)*d(x))

Solution

1. Identify the integral as a trigonometric function with a linear composition a*x where a=2

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

3. Substitute the value a=2 into the formula.

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

Final Answer

(∫_^)(sin(2*x)*d(x))=−1/2*cos(2*x)+C

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