Intergrate sin3x dx

To integrate sin(3x), you can use the substitution method.

Let's start by making a substitution:

Let u = 3x

Now, we can differentiate both sides of this equation with respect to x to find du/dx:

du/dx = 3

Rearranging this equation, we get:

dx = du/3

Now, substitute the value of dx in terms of du into the integral:

∫ sin(3x) dx = ∫ sin(u) (du/3)

This can be simplified as:

(1/3) ∫ sin(u) du

Integrating sin(u) gives us:

(1/3) [-cos(u)] + C

Finally, substitute back the value of u:

(1/3) [-cos(3x)] + C

So, the integral of sin(3x) is (1/3) [-cos(3x)] + C, where C is the constant of integration.