What is the value of arcsinh((e^8-1)/(2e^4)) ?

The value of arcsinh((e^8-1)/(2e^4)) is ln((e^8-1+sqrt(e^{16)+2e^8+1})/(2e^4))

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arcsinh((e^8-1)/(2e^4))

arcsinh (\frac{e ^{8} - 1}{2 e ^{4}})

ln (\frac{e ^{8} - 1 + e ^{16} + 2 e ^{8} + 1}{2 e ^{4}})

Solution steps

arcsinh (\frac{e ^{8} - 1}{2 e ^{4}})

Use the Hyperbolic identity:

arcsinh (x) = ln (x + x^{2} + 1)

= ln \frac{e ^{8} - 1}{2 e ^{4}} + (\frac{e ^{8} - 1}{2 e ^{4}})^{2} + 1

ln \frac{e ^{8} - 1}{2 e ^{4}} + (\frac{e ^{8} - 1}{2 e ^{4}})^{2} + 1 = ln (\frac{e ^{8} - 1 + e ^{16} + 2 e ^{8} + 1}{2 e ^{4}})

= ln (\frac{e ^{8} - 1 + e ^{16} + 2 e ^{8} + 1}{2 e ^{4}})

csc^{2} (3 0^{\circ}) - cot^{2} (4 5^{\circ})

ln (sec (1))

1 sin (1) - 1

1 arctan (1)

cot (4 3^{\circ})

What is the value of arcsinh((e^8-1)/(2e^4)) ?
The value of arcsinh((e^8-1)/(2e^4)) is ln((e^8-1+sqrt(e^{16)+2e^8+1})/(2e^4))