Word Count : 284

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हम अवशिष्ट (Residue) विधि का उपयोग करके निम्नलिखित समाकलन को हल करेंगे: [ \int_0^\infty \frac{dx}{x^2 + 1}. ] चरण 1: समाकलन को जटिल विमा में व्यक्त करें परिकल्पना करें कि [ f(z) = \frac{1}{z^2 + 1} = \frac{1}{(z-i)(z+i)} ] एक जटिल चर ( z ) के लिए। हम ( z )-समतल में एक अर्धवृत्तीय पथ ( _________ ______ __________ ______ _______ ____ __________ ______ ____ _____ _________.
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