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

Problem

(∫_^)(5*sin(x)*d(x))

Solution

1. Apply the constant multiple rule by moving the constant factor 5 outside of the integral.

(∫_^)(5*sin(x)*d(x))=5*(∫_^)(sin(x)*d(x))

2. Apply the integration rule for the sine function, which states that (∫_^)(sin(x)*d(x))=−cos(x)

5*(∫_^)(sin(x)*d(x))=5*(−cos(x))+C

3. Simplify the expression by multiplying the constant and the trigonometric function.

5*(−cos(x))+C=−5*cos(x)+C

Final Answer

(∫_^)(5*sin(x)*d(x))=−5*cos(x)+C

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