3.94.98 \(\int 6 e^{e^3 (20+8 e)} \, dx\) [9398]

Optimal. Leaf size=18 \[ 3+6 e^{\left (8+\frac {20}{e}\right ) e^4} x \]

[Out]

6*x*exp((8+20/exp(1))*exp(4))+3

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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.83, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \begin {gather*} 6 e^{4 e^3 (5+2 e)} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6*E^(E^3*(20 + 8*E)),x]

[Out]

6*E^(4*E^3*(5 + 2*E))*x

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=6 e^{4 e^3 (5+2 e)} x\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.78 \begin {gather*} 6 e^{e^3 (20+8 e)} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6*E^(E^3*(20 + 8*E)),x]

[Out]

6*E^(E^3*(20 + 8*E))*x

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Maple [A]
time = 0.02, size = 18, normalized size = 1.00

method	result	size
risch	\(6 x \,{\mathrm e}^{8 \,{\mathrm e}^{4}+20 \,{\mathrm e}^{3}}\)	\(14\)
default	\(6 x \,{\mathrm e}^{\left (8 \,{\mathrm e}+20\right ) {\mathrm e}^{4} {\mathrm e}^{-1}}\)	\(18\)
norman	\(6 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} {\mathrm e}^{20 \,{\mathrm e}^{3}} x\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x,method=_RETURNVERBOSE)

[Out]

6*x*exp((8*exp(1)+20)*exp(4)/exp(1))

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Maxima [A]
time = 0.26, size = 14, normalized size = 0.78 \begin {gather*} 6 \, x e^{\left (4 \, {\left (2 \, e + 5\right )} e^{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="maxima")

[Out]

6*x*e^(4*(2*e + 5)*e^3)

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Fricas [A]
time = 0.36, size = 13, normalized size = 0.72 \begin {gather*} 6 \, x e^{\left (8 \, e^{4} + 20 \, e^{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="fricas")

[Out]

6*x*e^(8*e^4 + 20*e^3)

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Sympy [A]
time = 0.01, size = 14, normalized size = 0.78 \begin {gather*} 6 x e^{\left (20 + 8 e\right ) e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x)

[Out]

6*x*exp((20 + 8*E)*exp(3))

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Giac [A]
time = 0.42, size = 14, normalized size = 0.78 \begin {gather*} 6 \, x e^{\left (4 \, {\left (2 \, e + 5\right )} e^{3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="giac")

[Out]

6*x*e^(4*(2*e + 5)*e^3)

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Mupad [B]
time = 0.00, size = 13, normalized size = 0.72 \begin {gather*} 6\,x\,{\mathrm {e}}^{{\mathrm {e}}^3\,\left (8\,\mathrm {e}+20\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*exp(exp(3)*(8*exp(1) + 20)),x)

[Out]

6*x*exp(exp(3)*(8*exp(1) + 20))

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