Descargar Gratis Revistas De Condorito En Pdf

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Uveřejněné: 16.10.2022 (více jak 4 měsíci)


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Descargar Gratis Revistas De Condorito En Pdf

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Definite integration with substitution and complex numbers

I would like to evaluate $$intint_{R}frac{1}{(sin z+cos z)(cosh z+sinh z)}dz tag{1}$$ where $R$ is the region
$$Re(z)>0,quad Im(z)>0$$

My attempt:
I have found the region $R$ which is bounded by
$$Re(z)>0,quad Im(z)>0implies (z, sin(z), cos(z), sinh(z), cosh(z))$$
Now, I am lost in the following steps:
$$intint_{R}frac{1}{(sin z+cos z)(cosh z+sinh z)}dz$$
$$frac{1}{2}intint_{R}frac{1}{(sin z+cos z)(cosh z+sinh z)}dz$$
$$frac{1}{2}intint_{R}frac{1}{(sin z+cos z)(cosh z+sinh z)}dz$$
$$intint_{D}frac{1}{(sin z+cos z)(cosh z+sinh z)}dz$$
Where $D$ is the region
$$Re(z)>0,quad Im(z)>0implies (z, z^2, z^4, z^6,z^8)$$
Please help me find the answer.

A:

We have
$$int_{0}^{2pi}frac{1}{(sin z+cos z)(cosh z+sinh z)},dz$$

Note that
$$(sin z+cos z)(cosh z+sinh z)=sinh^2z+cos^2z+cosh^2z+sinh^2z=
c6a93da74d

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