Evaluate the Integral integral of 3cos(x) with respect to x

Problem

(∫_^)(3*cos(x)*d(x))

Solution

1. Identify the constant multiple rule for integration, which allows the constant 3 to be moved outside the integral.

(∫_^)(3*cos(x)*d(x))=3*(∫_^)(cos(x)*d(x))

2. Apply the basic integration rule for the cosine function, which states that the integral of cos(x) is sin(x)

(∫_^)(cos(x)*d(x))=sin(x)+C

3. Multiply the result by the constant 3 and include the constant of integration C

3*(sin(x))+C=3*sin(x)+C

Final Answer

(∫_^)(3*cos(x)*d(x))=3*sin(x)+C

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