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

Problem

(∫_^)(cos(x/5)*d(x))

Solution

1. Identify the form of the integral, which is a basic trigonometric function with a linear argument a*x where a=1/5

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 value a=1/5 into the formula.

4. Simplify the coefficient by calculating the reciprocal of 1/5 which is 5

Final Answer

(∫_^)(cos(x/5)*d(x))=5*sin(x/5)+C

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