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.