How do you find the integral of a trigonometric function like sin(x)?

To find the integral of a trigonometric function like sin(x), the most effective approach is to use the antiderivative associated with it.

The antiderivative of sin(x) is a standard result in integral calculus and is known to be -cos(x) + C, where C is the constant of integration. This is because integration is essentially the reverse process of differentiation, and knowing the derivative of sin(x) helps in identifying the correct antiderivative.

The other methods mentioned, such as finding the derivative first, using logarithmic properties, or employing exponential identities, are not applicable to directly integrating a simple function like sin(x). While there are instances where logarithmic and exponential properties can aid in evaluating more complex integrals, they do not apply to the basic integration of sin(x) in a straightforward sense. Therefore, utilizing the known antiderivative is the most appropriate and efficient method for this scenario.