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I am trying to teach myself complex analysis . There seems to be multiple ways of achieving the same thing and I am unsure on which approach to take, I am also struggling to visualise the problem...Would someone show me step by step how to solve for example

$$\int_{\Gamma}\frac{2\lambda}{[(\lambda-\lambda_{+})(\lambda-\lambda_{-})]^{2}}\frac{d\lambda}{i}$$

where ##\lambda_{+}, \ \ \lambda_{-}## are the roots given by

##\lambda_{\pm}=\frac{-i\zeta\pm ir}{q}##

So i believe the answer should be ##\frac{x}{r^{3}}## or something like that but I can't get there. Could someone show me how to approach a problem like this... Like visualise the contour etc

$$\int_{\Gamma}\frac{2\lambda}{[(\lambda-\lambda_{+})(\lambda-\lambda_{-})]^{2}}\frac{d\lambda}{i}$$

where ##\lambda_{+}, \ \ \lambda_{-}## are the roots given by

##\lambda_{\pm}=\frac{-i\zeta\pm ir}{q}##

So i believe the answer should be ##\frac{x}{r^{3}}## or something like that but I can't get there. Could someone show me how to approach a problem like this... Like visualise the contour etc

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