proving integration of 1/x^2+1 using cmplx nbumbers? (1 Viewer)

Average Boreduser · Mar 15, 2024

my teacher said u can prove int(1/x^2+1)= tan^-1x+C using complex numbers?? Can someone guide me here? I have a general idea as to how it should maybe work? I used partial fractions but in the end i got -tan^-1(1/x)+C and Idk what to do from there nor do ik if this is even rightspojdfiknlv

tywebb · Mar 15, 2024

Luukas.2 · Mar 15, 2024

Average Boreduser said:
my teacher said u can prove int(1/x^2+1)= tan^-1x+C using complex numbers?? Can someone guide me here? I have a general idea as to how it should maybe work? I used partial fractions but in the end i got -tan^-1(1/x)+C and Idk what to do from there nor do ik if this is even rightspojdfiknlv

$\text{Since} \qquad \tan^{-1}{x} + \tan^{-1}{\left(\frac{1}{x}\right)} = \frac{\pi}{2} \qquad \text{for all $x > 0$}$

$\text{And} \qquad \tan^{-1}{x} + \tan^{-1}{\left(\frac{1}{x}\right)} = -\frac{\pi}{2} \qquad \text{for all $x < 0$}$

$\text{Your answer and the desired answer match but with different constants of integration (provided $0 \notin $ Domain) and so are equivalent.}$

proving integration of 1/x^2+1 using cmplx nbumbers? (1 Viewer)

Average Boreduser

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tywebb

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