I need help with integral of 2x - 3cos2x please

Question

anonymous · Answer

specifically the trig...

trojanpoem · Answer

Notice that the Integration of cosx = sinx, x^n = x^n+1/ n+1 , Let's start :

$$\int\limits_{}^{} 2x - 2\cos2x = \frac{ 2x^2 }{ 2 } - \frac{  2\sin(2x) }{ 2 } + c$$

$$x^2 - \sin(2x) + c$$

trojanpoem · Answer

After integrating , it's recommended to check if your answer is right ( 99.5 this check works)  get the derivative. If both the question and your derivative are equal be sure you are.

anonymous · Answer

looks like you may have misread the problem? Here's what wolfram gave us: http://www.wolframalpha.com/input/?i=integral+of+2x+-+3cos2x

trojanpoem · Answer

my bad just replace 2/2 with 3/2 
so you have x^2 - 3/2 sin2x + c 
wolframalpha just used double angle rule sin2x = 2sinxcos 
so x^2 - 3sinxcosx + c

trojanpoem · Answer

To me , keep it sin(2x)

anonymous · Answer

@TrojanPoem , can you break it down further?

welshfella · Answer

No you cant break it down any further

anonymous · Answer

got it, beginning to reason through the heuristics of inverse reasoning, although slowly