Integrate sin(4x+π/6) dx

Answer 1

Using the substitution u = 4x + π/6, du/dx = 4, dx = du/4. Therefore,

∫sin(4x+π/6) dx = ∫sin(u) (1/4) du

Integrating sin(u) gives -cos(u) + C, where C is the constant of integration. Substituting u back in gives:

- (1/4)cos(4x + π/6) + C

So the final answer is:

∫sin(4x+π/6) dx = -(1/4)cos(4x + π/6) + C