# What is the antiderivative of #sin(4t) #?

It is:

The best I can do is pick one or two and explain using those of the numerous methods and notations that may or may not have been introduced to students at the time this question was posed:

The best course of action is to think like this:

As a result of the Mean Value Theorem, any function with the same derivative deviates from this by only a constant.

(If you haven't already, you will likely be introduced to the standard "u-substitution" mechanics; however, that is merely the mechanics behind the previously stated reasoning.)

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The antiderivative of sin(4t) is -(1/4)cos(4t) + C, where C is the constant of integration.

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