4) ׬ 6 sin(6𝑥) 𝑑𝑥

The integral of 6sin(6x) dx can be solved using the method of substitution. Here are the steps:

1. Let u = 6x. Then, du/dx = 6, or equivalently, dx = du/6.

2. Substitute these into the integral, to get ∫ sin(u) * (du/6).

3. The integral of sin(u) is -cos(u), so the integral becomes -cos(u)/6.

4. Substitute u = 6x back in to get the final answer: -cos(6x)/6 + C, where C is the constant of integration.

It seems like you want to integrate the function 6sin(6x) dx. Here are the steps:

1. Recognize that this is an integral of the form ∫a*sin(bx) dx, where a = 6 and b = 6.

2. The integral of sin(bx) dx is -(1/b)cos(bx) + C, where C is the constant of integration.

3. Therefore, the integral of asin(bx) dx is -a(1/b)cos(bx) + C.

4. Substituting a = 6 and b = 6, we get -6*(1/6)cos(6x) + C.

5. Simplifying, we get -cos(6x) + C.

So, ∫6sin(6x) dx = -cos(6x) + C.