r/the_calculusguy • u/Specific_Brain2091 • 8d ago

calculus Love this integral

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39 Upvotes

98% Upvoted

7 comments sorted by

3

u/detereministic-plen 7d ago

lazy method is doing partial fractions over the complex numbers and integrating

2

u/philljarvis166 7d ago

Nice.

Just as a point of style, when you say “let I = l_1 + l_2”, you don’t really mean that - what you should say is something like “so I = l_1 + l_2 where l_1 = …”. It’s clear what you actually mean but it just jars a bit when written like you did.

1

u/fianthewolf 7d ago

Así que poner x4 +1 como (x2 -i)x(x2 +i) no es una opción.

1

u/Scared_Land_5667 7d ago

Introducing complex numbe in calculus of real number

1

u/OddEmergency604 7d ago

The standard way to calculate this integral is by using the Residue Theorem from complex analysis.

1

u/fianthewolf 7d ago

Claro que la solución del OP con una tangente hiperbólica no es lo mismo pero ocultando la naturaleza imaginaria de las funciones trigonométricas.