Evaluate the Integral integral of 2cos(2x) with respect to x

Problem

(∫_^)(2*cos(2*x)*d(x))

Solution

1. Identify the constant and the function to be integrated. The constant 2 can be moved outside the integral.

(∫_^)(2*cos(2*x)*d(x))=2*(∫_^)(cos(2*x)*d(x))

2. Apply the rule for the integral of cos(a*x) which is (∫_^)(cos(a*x)*d(x))=sin(a*x)/a+C

2*(∫_^)(cos(2*x)*d(x))=2⋅sin(2*x)/2+C

3. Simplify the expression by canceling the 2 in the numerator and the denominator.

2⋅sin(2*x)/2+C=sin(2*x)+C

Final Answer

(∫_^)(2*cos(2*x)*d(x))=sin(2*x)+C

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