Optimal. Leaf size=36 \[ 6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.052147, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ 6 x-\frac{e^{-4 x}}{4}+2 e^{-2 x}-2 e^{2 x}+\frac{e^{4 x}}{4} \]
Antiderivative was successfully verified.
[In] Int[(-E^(-x) + E^x)^4,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 2 e^{2 x} + 3 \log{\left (e^{2 x} \right )} + \frac{\int ^{e^{2 x}} x\, dx}{2} + 2 e^{- 2 x} - \frac{e^{- 4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-1/exp(x)+exp(x))**4,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0234141, size = 34, normalized size = 0.94 \[ \frac{1}{4} \left (24 x-e^{-4 x}+8 e^{-2 x}-8 e^{2 x}+e^{4 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-E^(-x) + E^x)^4,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 31, normalized size = 0.9 \[{\frac{ \left ({{\rm e}^{x}} \right ) ^{4}}{4}}-2\, \left ({{\rm e}^{x}} \right ) ^{2}-{\frac{1}{4\, \left ({{\rm e}^{x}} \right ) ^{4}}}+2\, \left ({{\rm e}^{x}} \right ) ^{-2}+6\,\ln \left ({{\rm e}^{x}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-1/exp(x)+exp(x))^4,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35233, size = 38, normalized size = 1.06 \[ 6 \, x + \frac{1}{4} \, e^{\left (4 \, x\right )} - 2 \, e^{\left (2 \, x\right )} + 2 \, e^{\left (-2 \, x\right )} - \frac{1}{4} \, e^{\left (-4 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(-x) - e^x)^4,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.203782, size = 42, normalized size = 1.17 \[ \frac{1}{4} \,{\left (24 \, x e^{\left (4 \, x\right )} + e^{\left (8 \, x\right )} - 8 \, e^{\left (6 \, x\right )} + 8 \, e^{\left (2 \, x\right )} - 1\right )} e^{\left (-4 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(-x) - e^x)^4,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.153951, size = 31, normalized size = 0.86 \[ 6 x + \frac{e^{4 x}}{4} - 2 e^{2 x} + 2 e^{- 2 x} - \frac{e^{- 4 x}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-1/exp(x)+exp(x))**4,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.198424, size = 49, normalized size = 1.36 \[ -\frac{1}{4} \,{\left (18 \, e^{\left (4 \, x\right )} - 8 \, e^{\left (2 \, x\right )} + 1\right )} e^{\left (-4 \, x\right )} + 6 \, x + \frac{1}{4} \, e^{\left (4 \, x\right )} - 2 \, e^{\left (2 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e^(-x) - e^x)^4,x, algorithm="giac")
[Out]