I need the solution steps for this integral as soon as possible. Please this is an emergency!
PROBLEM: integrate e^(7ix)*((e^(2ix)+e^(-2ix))/2) dx
More specifically, can you send me the steps integrating the function using complex integrals
i.e. cos(2x) = [e^(2ix) + e^(-2ix)]/2
i.e. sin(2x)= [e^(2ix) - e^(-2ix)]/2i
Try replacing “i” with an undefined variable and then integrate. You can probably have Wolfram|Alpha do these integrals and give you the step by step instructions on how to solve them. After that, substitute the “i” back in the equation and do some algebraic simplification.
Doing integrals with complex numbers is not significantly more complex than doing them with real values.
Make sure you using the right Mathematica syntax:
Integrate[E^(7 I x). . . , Sin[2x], etc.
Here’s the code that appears to work:
In[11]:= Integrate[E^(7 I x)*((E^(2 I x) + E^(-2 I x))/2), x]
Out[11]= -(1/90) I E^(5 I x) (9 + 5 E^(4 I x))