3.705 \(\int e^x \left (-e^{-x}+e^x\right )^2 \, dx\)

Optimal. Leaf size=22 \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]

[Out]

-E^(-x) - 2*E^x + E^(3*x)/3

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Rubi [A]  time = 0.0461803, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]

Antiderivative was successfully verified.

[In]  Int[E^x*(-E^(-x) + E^x)^2,x]

[Out]

-E^(-x) - 2*E^x + E^(3*x)/3

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Rubi in Sympy [A]  time = 14.5517, size = 15, normalized size = 0.68 \[ \frac{e^{3 x}}{3} - 2 e^{x} - e^{- x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x)*(-1/exp(x)+exp(x))**2,x)

[Out]

exp(3*x)/3 - 2*exp(x) - exp(-x)

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Mathematica [A]  time = 0.00934958, size = 22, normalized size = 1. \[ -e^{-x}-2 e^x+\frac{e^{3 x}}{3} \]

Antiderivative was successfully verified.

[In]  Integrate[E^x*(-E^(-x) + E^x)^2,x]

[Out]

-E^(-x) - 2*E^x + E^(3*x)/3

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Maple [A]  time = 0.006, size = 18, normalized size = 0.8 \[{\frac{ \left ({{\rm e}^{x}} \right ) ^{3}}{3}}-2\,{{\rm e}^{x}}- \left ({{\rm e}^{x}} \right ) ^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(x)*(-1/exp(x)+exp(x))^2,x)

[Out]

1/3*exp(x)^3-2*exp(x)-1/exp(x)

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Maxima [A]  time = 0.775132, size = 28, normalized size = 1.27 \[ -\frac{1}{3} \,{\left (6 \, e^{\left (-2 \, x\right )} - 1\right )} e^{\left (3 \, x\right )} - e^{\left (-x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e^(-x) - e^x)^2*e^x,x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.236467, size = 24, normalized size = 1.09 \[ \frac{1}{3} \,{\left (e^{\left (4 \, x\right )} - 6 \, e^{\left (2 \, x\right )} - 3\right )} e^{\left (-x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e^(-x) - e^x)^2*e^x,x, algorithm="fricas")

[Out]

1/3*(e^(4*x) - 6*e^(2*x) - 3)*e^(-x)

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Sympy [A]  time = 0.109789, size = 15, normalized size = 0.68 \[ \frac{e^{3 x}}{3} - 2 e^{x} - e^{- x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x)*(-1/exp(x)+exp(x))**2,x)

[Out]

exp(3*x)/3 - 2*exp(x) - exp(-x)

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GIAC/XCAS [A]  time = 0.224113, size = 23, normalized size = 1.05 \[ \frac{1}{3} \, e^{\left (3 \, x\right )} - e^{\left (-x\right )} - 2 \, e^{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e^(-x) - e^x)^2*e^x,x, algorithm="giac")

[Out]

1/3*e^(3*x) - e^(-x) - 2*e^x