Find the following indefinite integral:∫(4cos(𝑥))d𝑥=

The indefinite integral of a function is its antiderivative, or the original function that was differentiated to get the given function.

The integral of cos(x) is sin(x), and the constant multiple rule of integration states that the integral of a constant times a function is equal to the constant times the integral of the function.

So, to find the indefinite integral of 4cos(x) dx, you would multiply the integral of cos(x) by 4.

Here are the steps:

1. Identify the function to be integrated, which is 4cos(x).
2. Recognize that the integral of cos(x) is sin(x).
3. Apply the constant multiple rule to get 4 times the integral of cos(x), which is 4sin(x).
4. Add the constant of integration, usually denoted as C, to account for the fact that the antiderivative is only unique up to a constant.

So, ∫4cos(x) dx = 4sin(x) + C.