Evaluate the Integral integral of cos(5x) with respect to x

Problem

(∫_^)(cos(5*x)*d(x))

Solution

1. Identify the integral form as a basic trigonometric integral of the type (∫_^)(cos(a*x)*d(x))

2. Apply the formula for the integral of cos(a*x) which is 1/a*sin(a*x)+C

3. Substitute the value a=5 into the formula.

4. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(cos(5*x)*d(x))=1/5*sin(5*x)+C

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