Find the Derivative of the Integral integral of cos(x)^5 with respect to x

Problem

d()/d(x)*(∫_^)(cos(x)*d(x))

Solution

1. Identify the structure of the problem as the derivative of an indefinite integral.

2. Apply the Fundamental Theorem of Calculus, which states that the derivative of an integral of a function is the original function itself.

3. Simplify the expression by removing the integral and derivative operators, as they are inverse operations.

Final Answer

d()/d(x)*(∫_^)(cos(x)*d(x))=cos(x)

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