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To integrate e^(-2x)dx, you need to take a u substitution.
u=-2x
du=-2dx
Since the original integral does not have a -2 in it, you need to divide to get the dx alone.
-(1/2)du=dx
Since the integral of e^x is still e^x, you get:
y = -(1/2)e^(-2x)
Well, that was one method. I usually solve easier functions like this by thinking how the function looked like before it was differentiated. I let f(x) stand for the given function and F(x) stand for the primitive function; the function we had before differentiation (the integrated function).
f(x)= e-2x <-- our given function
F(x)= e-2x/-2 <-- our integrated function
Evidence: F'(x)= -2e-2x/-2 = e-2x = f(x) Q.E.D
It's as simple as that.
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