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

Problem

(∫_^)(sin(5*x)*d(x))

Solution

1. Identify the integral form as a trigonometric function with a linear argument a*x where a=5

2. Apply the rule for the integral of sin(a*x) which is (∫_^)(sin(a*x)*d(x))=−1/a*cos(a*x)+C

3. Substitute the value a=5 into the formula to find the antiderivative.

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

Final Answer

(∫_^)(sin(5*x)*d(x))=−1/5*cos(5*x)+C

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