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Please help with this integral: ∫sin(e^(-2x)) / e^(2x) dx. With steps if possible and thank you.

 Jun 12, 2017
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Take the integral:
 integral e^(-2 x) sin(e^(-2 x)) dx
For the integrand e^(-2 x) sin(e^(-2 x)), substitute u = -2 x and du = -2 dx:
 = -1/2 integral e^u sin(e^u) du
For the integrand e^u sin(e^u), substitute s = e^u and ds = e^u du:
 = -1/2 integral sin(s) ds
The integral of sin(s) is -cos(s):
 = (cos(s))/2 + constant
Substitute back for s = e^u:
 = (cos(e^u))/2 + constant
Substitute back for u = -2 x:
Answer: | = 1/2 cos(e^(-2 x)) + constant

 Jun 12, 2017

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