Question

Integration of $1/(1-x^2)$ to prove $\operatorname{arctanh}(x)$

score 1.6k · Answer 1 · 2019-04-12 11:44:43

Integration of $1/(1-x^2)$ to prove $\operatorname{arctanh}(x)$

Published on 12 Apr 2019 - 11:44

score 185 · Answer 2 · 2019-04-12 17:51:33

Time difference of arrival - obtaining a hyperbola from equations, I have the starting values but I'm super confused with the equations.

score 90 · Answer 3 · 2019-04-17 20:38:54

90

Views

Evaluate the following integral using the substitution $x=9\sinh^2\theta$ $\int_0^1\sqrt{\frac{x+9}{x}}dx$

Published on 17 Apr 2019 - 20:38

score 66 · Answer 4 · 2019-04-20 11:31:17

66

Views

Prove that $\sum_{n=0}^\infty {\frac{x^{2n+1}}{(2n+1)!}} = \frac{e^x - e^{-x}}{2}$

Published on 20 Apr 2019 - 11:31

score 121 · Answer 5 · 2019-04-25 00:56:32

121

Views

Completing a proof of a formula for the area of a hyperbolic right triangle

Published on 25 Apr 2019 - 0:56

score 123 · Answer 6 · 2019-04-26 20:32:53

123

Views

Showing $\lvert\cos z\rvert^2=a\cos2x+b\cosh2y$, where $z=x+iy$, for numbers $a$ and $b$ to be determined

Published on 26 Apr 2019 - 20:32

score 31 · Answer 7 · 2019-05-08 10:26:14

31

Views

Getting the general solution to $G''(x) - c G(x) = 0$, for $(c\neq 0)$, in the form of hyperbolic/trigonometric functions

Published on 08 May 2019 - 10:26

score 346 · Answer 8 · 2019-05-09 20:31:34

346

Views

Exponential of Matrix Rewritten as Hyperbolic Functions

Published on 09 May 2019 - 20:31

score 216 · Answer 9 · 2019-05-16 15:20:39

216

Views

Get arsinh from sinh

Published on 16 May 2019 - 15:20

score 101 · Answer 10 · 2019-05-16 20:23:50

101

Views

How do I show this hyperbolic integral: $ \int_0^1 \sinh(2x)dx= \frac14 (e-\frac1e)^2$

Published on 16 May 2019 - 20:23

score 30 · Answer 11 · 2019-05-17 12:44:53

30

Views

Taylor expansion of fraction involving hyperbolic functions

Published on 17 May 2019 - 12:44

score 98 · Answer 12 · 2019-05-18 13:11:42

98

Views

Finding the root of a transcendental equation involving $\cosh$

Published on 18 May 2019 - 13:11

score 280 · Answer 13 · 2019-05-26 07:50:38

280

Views

Show that the $n$-th Fibonacci number is given by $\frac{\cosh na}{\cosh a}$ or $\frac{\sinh na}{\cosh a}$, where $\sinh a=1/2$

Published on 26 May 2019 - 7:50

score 56 · Answer 14 · 2019-05-26 13:17:13

56

Views

How to "see" this algebraic transformation used to derive the exponential form of the hyperbolic cosine?

Published on 26 May 2019 - 13:17

score 246 · Answer 15 · 2026-02-23 05:43:27

246

Views

Inverse Laplace Transform of $\frac{1}{\lambda\cosh(\sqrt{as}+\sqrt{bs})+(1-\lambda)\cosh(\sqrt{as}-\sqrt{bs})}$.

Published on 23 Feb 2026 - 5:43

List Question

Integration of $1/(1-x^2)$ to prove $\operatorname{arctanh}(x)$

Time difference of arrival - obtaining a hyperbola from equations, I have the starting values but I'm super confused with the equations.

Evaluate the following integral using the substitution $x=9\sinh^2\theta$ $\int_0^1\sqrt{\frac{x+9}{x}}dx$

Prove that $\sum_{n=0}^\infty {\frac{x^{2n+1}}{(2n+1)!}} = \frac{e^x - e^{-x}}{2}$

Completing a proof of a formula for the area of a hyperbolic right triangle

Showing $\lvert\cos z\rvert^2=a\cos2x+b\cosh2y$, where $z=x+iy$, for numbers $a$ and $b$ to be determined

Getting the general solution to $G''(x) - c G(x) = 0$, for $(c\neq 0)$, in the form of hyperbolic/trigonometric functions

Exponential of Matrix Rewritten as Hyperbolic Functions

Get arsinh from sinh

How do I show this hyperbolic integral: $ \int_0^1 \sinh(2x)dx= \frac14 (e-\frac1e)^2$

Taylor expansion of fraction involving hyperbolic functions

Finding the root of a transcendental equation involving $\cosh$

Show that the $n$-th Fibonacci number is given by $\frac{\cosh na}{\cosh a}$ or $\frac{\sinh na}{\cosh a}$, where $\sinh a=1/2$

How to "see" this algebraic transformation used to derive the exponential form of the hyperbolic cosine?

Inverse Laplace Transform of $\frac{1}{\lambda\cosh(\sqrt{as}+\sqrt{bs})+(1-\lambda)\cosh(\sqrt{as}-\sqrt{bs})}$.

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