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latentcorpse

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Find [itex]\int_{\gamma} e^{\sin{z}} \cos{z} dz[/itex]

this is holomorphic on the entire copmlex plan so we can't use a residue theorem. furthermore, we can't assume [itex]\gamma[/itex] is a closed contour as we aren't told [itex]w_1=w_2[/itex] so it looks as if we're going to need to parameterise [itex]\gamma[/itex].

but we don't know what [itex]\gamma[/itex] looks like. however we do know that any two point in the copmlex plane can be joined by a finite number of horizontal and vertical lines so if we use instead of [itex]\gamma[/itex] a contour [itex]\gamma_1 \cup \gamma_2[/itex]

where [itex]\gamma_1[/itex] is horizontal and [itex]\gamma_2[/itex] is vertical. this is my thoughts so far but parameterising these was still going to be pretty difficult so i decided to check if im on the right lines or not. any advice?