Evaluate the Integral integral of cos(7x) with respect to x

Problem

(∫_^)(cos(7*x)*d(x))

Solution

1. Identify the integral form as a basic trigonometric integral requiring a substitution or the reverse chain rule for a linear argument a*x

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

3. Substitute the constant a=7 into the formula.

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

Final Answer

(∫_^)(cos(7*x)*d(x))=1/7*sin(7*x)+C

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