3.261 \(\int e^{e^x+x} \, dx\)

Optimal. Leaf size=5 \[ e^{e^x} \]

[Out]

E^E^x

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Rubi [A]  time = 0.00952141, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ e^{e^x} \]

Antiderivative was successfully verified.

[In]  Int[E^(E^x + x),x]

[Out]

E^E^x

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Rubi in Sympy [A]  time = 1.97641, size = 3, normalized size = 0.6 \[ e^{e^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(x+exp(x)),x)

[Out]

exp(exp(x))

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Mathematica [A]  time = 0.00302928, size = 5, normalized size = 1. \[ e^{e^x} \]

Antiderivative was successfully verified.

[In]  Integrate[E^(E^x + x),x]

[Out]

E^E^x

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Maple [A]  time = 0.003, size = 4, normalized size = 0.8 \[{{\rm e}^{{{\rm e}^{x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(exp(x)+x),x)

[Out]

exp(exp(x))

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Maxima [A]  time = 1.3295, size = 4, normalized size = 0.8 \[ e^{\left (e^{x}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

e^(e^x)

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Fricas [A]  time = 0.205278, size = 4, normalized size = 0.8 \[ e^{\left (e^{x}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

e^(e^x)

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Sympy [A]  time = 0.597229, size = 3, normalized size = 0.6 \[ e^{e^{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(x+exp(x)),x)

[Out]

exp(exp(x))

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GIAC/XCAS [A]  time = 0.206549, size = 4, normalized size = 0.8 \[ e^{\left (e^{x}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

e^(e^x)