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Evaluate $\int\frac{1}{x}\coth(ax)\sin^2(\frac{xt}{2})dx$

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#integration #definite-integrals #indefinite-integrals #hyperbolic-functions
103
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Law of Cosines with imaginary arguments?

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#geometry #trigonometry #hyperbolic-geometry #hyperbolic-functions
69
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Exponential Proof

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#algebra-precalculus #exponential-function #hyperbolic-functions
901
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Suppose $z=re^{iθ}$, prove : $|e^{iz}|=e^{-r\sinθ}$.

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#complex-analysis #hyperbolic-functions
2.2k
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How to simplify expressions like $\sinh(4\,\text{arcsinh}(x))$?

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#inverse #hyperbolic-functions
293
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A improper integral with integrable singularities

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#integration #hyperbolic-functions
74
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Hyperbolic trigonometric functions identity

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#calculus #hyperbolic-functions
106
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Find the limit as x approaches infinity

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#calculus #limits #hyperbolic-functions
2.2k
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Hint to show $\tanh(z)=\frac{\sinh(2x)+i\sin(2y)}{\cosh(2x)+\cos(2y)}$?

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#algebra-precalculus #complex-numbers #hyperbolic-functions
1.5k
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Curious about an empirically found continued fraction for tanh

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#number-theory #closed-form #continued-fractions #hyperbolic-functions
53
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Differentiate $[x^{5\coth(6x)}]'$

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#derivatives #hyperbolic-functions
41
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Hyperbolic sine of a logarithm

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#algebra-precalculus #exponential-function #hyperbolic-functions
237
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Is $ \sum_{n=1}\limits^{\infty}\frac{1}{\sinh(2^{n})} $ equal to $ \frac{2}{e^{2}-1}$?

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#calculus #sequences-and-series #hyperbolic-functions
10.8k
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How to solve lim as x approaches infinity for $[\tanh(x)]^x$

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#limits #hyperbolic-functions
179
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Relating the argument of a hyperbolic trig function to area

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#calculus #hyperbolic-functions

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