Question - Solving an Integral Involving a Trigonometric Function

The integral of \( f(x) = -3 \cos(4x) \) can be found using the standard integration techniques for trigonometric functions.

Let \( u = 4x \). Therefore, \( du = 4dx \) or \( \frac{du}{4} = dx \).

The integral becomes:

\( \int -3 \cos(4x) dx = \int -3 \cos(u) \frac{du}{4} \)

\( = -\frac{3}{4} \int \cos(u) du \)

\( = -\frac{3}{4} \sin(u) + C \)

Substituting back \( u = 4x \):

\( = -\frac{3}{4} \sin(4x) + C \)

Where \( C \) is the constant of integration.