3.498 \(\int \left (-e^{-x}+e^x\right )^3 \, dx\)

Optimal. Leaf size=31 \[ \frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3} \]

[Out]

1/(3*E^(3*x)) - 3/E^x - 3*E^x + E^(3*x)/3

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Rubi [A]  time = 0.0375142, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{e^{-3 x}}{3}-3 e^{-x}-3 e^x+\frac{e^{3 x}}{3} \]

Antiderivative was successfully verified.

[In]  Int[(-E^(-x) + E^x)^3,x]

[Out]

1/(3*E^(3*x)) - 3/E^x - 3*E^x + E^(3*x)/3

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Rubi in Sympy [A]  time = 3.53578, size = 24, normalized size = 0.77 \[ \frac{e^{3 x}}{3} - 3 e^{x} - 3 e^{- x} + \frac{e^{- 3 x}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-1/exp(x)+exp(x))**3,x)

[Out]

exp(3*x)/3 - 3*exp(x) - 3*exp(-x) + exp(-3*x)/3

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Mathematica [A]  time = 0.0124771, size = 30, normalized size = 0.97 \[ \frac{1}{3} e^{-3 x} \left (-9 e^{2 x}-9 e^{4 x}+e^{6 x}+1\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(-E^(-x) + E^x)^3,x]

[Out]

(1 - 9*E^(2*x) - 9*E^(4*x) + E^(6*x))/(3*E^(3*x))

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Maple [A]  time = 0.009, size = 24, normalized size = 0.8 \[{\frac{ \left ({{\rm e}^{x}} \right ) ^{3}}{3}}-3\,{{\rm e}^{x}}+{\frac{1}{3\, \left ({{\rm e}^{x}} \right ) ^{3}}}-3\, \left ({{\rm e}^{x}} \right ) ^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-1/exp(x)+exp(x))^3,x)

[Out]

1/3*exp(x)^3-3*exp(x)+1/3/exp(x)^3-3/exp(x)

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Maxima [A]  time = 1.3546, size = 31, normalized size = 1. \[ \frac{1}{3} \, e^{\left (3 \, x\right )} - 3 \, e^{\left (-x\right )} + \frac{1}{3} \, e^{\left (-3 \, x\right )} - 3 \, e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(e^(-x) - e^x)^3,x, algorithm="maxima")

[Out]

1/3*e^(3*x) - 3*e^(-x) + 1/3*e^(-3*x) - 3*e^x

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Fricas [A]  time = 0.201237, size = 32, normalized size = 1.03 \[ \frac{1}{3} \,{\left (e^{\left (6 \, x\right )} - 9 \, e^{\left (4 \, x\right )} - 9 \, e^{\left (2 \, x\right )} + 1\right )} e^{\left (-3 \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(e^(-x) - e^x)^3,x, algorithm="fricas")

[Out]

1/3*(e^(6*x) - 9*e^(4*x) - 9*e^(2*x) + 1)*e^(-3*x)

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Sympy [A]  time = 0.130581, size = 24, normalized size = 0.77 \[ \frac{e^{3 x}}{3} - 3 e^{x} - 3 e^{- x} + \frac{e^{- 3 x}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-1/exp(x)+exp(x))**3,x)

[Out]

exp(3*x)/3 - 3*exp(x) - 3*exp(-x) + exp(-3*x)/3

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GIAC/XCAS [A]  time = 0.200068, size = 34, normalized size = 1.1 \[ -\frac{1}{3} \,{\left (9 \, e^{\left (2 \, x\right )} - 1\right )} e^{\left (-3 \, x\right )} + \frac{1}{3} \, e^{\left (3 \, x\right )} - 3 \, e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(e^(-x) - e^x)^3,x, algorithm="giac")

[Out]

-1/3*(9*e^(2*x) - 1)*e^(-3*x) + 1/3*e^(3*x) - 3*e^x