Integral of e^(-x)cos(2x)dx.

I get as far as Integral of e^(-x)cos2xdx=1/2e^(-x)sin2x + 1/2integral(sin2x*e^(-x)dx). Then I find integral(sin2x*e^(-x)dx)=-1/2e^(-x)cos2x - 1/2 integral(cos2xe^(-x)dx).

Problem: integral(cos2xe^(-x)dx) is original integral. What am I supposed to do with it?

I get as far as Integral of e^(-x)cos2xdx=1/2e^(-x)sin2x + 1/2integral(sin2x*e^(-x)dx). Then I find integral(sin2x*e^(-x)dx)=-1/2e^(-x)cos2x - 1/2 integral(cos2xe^(-x)dx).

Problem: integral(cos2xe^(-x)dx) is original integral. What am I supposed to do with it?

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