Optimal. Leaf size=20 \[ \frac{8 e^{6 x}}{3 \left (1-e^{2 x}\right )^3} \]
[Out]
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Rubi [A] time = 0.0381935, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3 \[ \frac{8 e^{6 x}}{3 \left (1-e^{2 x}\right )^3} \]
Antiderivative was successfully verified.
[In] Int[E^(2*x)*Csch[x]^4,x]
[Out]
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Rubi in Sympy [A] time = 2.14405, size = 27, normalized size = 1.35 \[ - \frac{e^{2 x}}{3 \sinh ^{2}{\left (x \right )}} - \frac{e^{2 x} \cosh{\left (x \right )}}{3 \sinh ^{3}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(2*x)/sinh(x)**4,x)
[Out]
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Mathematica [A] time = 0.0120733, size = 29, normalized size = 1.45 \[ -\frac{8 \left (-3 e^{2 x}+3 e^{4 x}+1\right )}{3 \left (e^{2 x}-1\right )^3} \]
Antiderivative was successfully verified.
[In] Integrate[E^(2*x)*Csch[x]^4,x]
[Out]
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Maple [A] time = 0.11, size = 20, normalized size = 1. \[ - \left ( \tanh \left ( x \right ) \right ) ^{-2}-{\frac{1}{3\, \left ( \tanh \left ( x \right ) \right ) ^{3}}}- \left ( \tanh \left ( x \right ) \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(2*x)/sinh(x)^4,x)
[Out]
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Maxima [A] time = 1.3664, size = 30, normalized size = 1.5 \[ \frac{8}{3 \,{\left (3 \, e^{\left (-2 \, x\right )} - 3 \, e^{\left (-4 \, x\right )} + e^{\left (-6 \, x\right )} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*x)/sinh(x)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203387, size = 101, normalized size = 5.05 \[ -\frac{8 \,{\left (4 \, \cosh \left (x\right )^{2} + 4 \, \cosh \left (x\right ) \sinh \left (x\right ) + 4 \, \sinh \left (x\right )^{2} - 3\right )}}{3 \,{\left (\cosh \left (x\right )^{4} + 4 \, \cosh \left (x\right ) \sinh \left (x\right )^{3} + \sinh \left (x\right )^{4} + 2 \,{\left (3 \, \cosh \left (x\right )^{2} - 2\right )} \sinh \left (x\right )^{2} - 4 \, \cosh \left (x\right )^{2} + 4 \,{\left (\cosh \left (x\right )^{3} - \cosh \left (x\right )\right )} \sinh \left (x\right ) + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*x)/sinh(x)^4,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{2 x}}{\sinh ^{4}{\left (x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(2*x)/sinh(x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.23012, size = 32, normalized size = 1.6 \[ -\frac{8 \,{\left (3 \, e^{\left (4 \, x\right )} - 3 \, e^{\left (2 \, x\right )} + 1\right )}}{3 \,{\left (e^{\left (2 \, x\right )} - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(2*x)/sinh(x)^4,x, algorithm="giac")
[Out]