3.10.63 \(\int e^{e^{e^x+2 x}+8 x \log (6)} (e^{e^x+2 x} (2+e^x)+8 \log (6)) \, dx\)

Optimal. Leaf size=17 \[ e^{e^{e^x+2 x}+8 x \log (6)} \]

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Rubi [A]  time = 0.16, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6706} \begin {gather*} 6^{8 x} e^{e^{2 x+e^x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(E^(E^x + 2*x) + 8*x*Log[6])*(E^(E^x + 2*x)*(2 + E^x) + 8*Log[6]),x]

[Out]

6^(8*x)*E^E^(E^x + 2*x)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=6^{8 x} e^{e^{e^x+2 x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 17, normalized size = 1.00 \begin {gather*} 6^{8 x} e^{e^{e^x+2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(E^(E^x + 2*x) + 8*x*Log[6])*(E^(E^x + 2*x)*(2 + E^x) + 8*Log[6]),x]

[Out]

6^(8*x)*E^E^(E^x + 2*x)

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fricas [A]  time = 0.58, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (8 \, x \log \relax (6) + e^{\left (2 \, x + e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+2)*exp(exp(x)+2*x)+8*log(6))*exp(exp(exp(x)+2*x)+8*x*log(6)),x, algorithm="fricas")

[Out]

e^(8*x*log(6) + e^(2*x + e^x))

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giac [A]  time = 0.30, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (8 \, x \log \relax (6) + e^{\left (2 \, x + e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+2)*exp(exp(x)+2*x)+8*log(6))*exp(exp(exp(x)+2*x)+8*x*log(6)),x, algorithm="giac")

[Out]

e^(8*x*log(6) + e^(2*x + e^x))

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maple [A]  time = 0.04, size = 15, normalized size = 0.88

method	result	size
derivativedivides	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}+2 x}+8 x \ln \relax (6)}\)	\(15\)
default	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}+2 x}+8 x \ln \relax (6)}\)	\(15\)
norman	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}+2 x}+8 x \ln \relax (6)}\)	\(15\)
risch	\(6561^{x} 256^{x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}+2 x}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp(x)+2)*exp(exp(x)+2*x)+8*ln(6))*exp(exp(exp(x)+2*x)+8*x*ln(6)),x,method=_RETURNVERBOSE)

[Out]

exp(exp(exp(x)+2*x)+8*x*ln(6))

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maxima [A]  time = 0.53, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (8 \, x \log \relax (6) + e^{\left (2 \, x + e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+2)*exp(exp(x)+2*x)+8*log(6))*exp(exp(exp(x)+2*x)+8*x*log(6)),x, algorithm="maxima")

[Out]

e^(8*x*log(6) + e^(2*x + e^x))

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mupad [B]  time = 0.74, size = 15, normalized size = 0.88 \begin {gather*} 6^{8\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(2*x + exp(x)) + 8*x*log(6))*(8*log(6) + exp(2*x + exp(x))*(exp(x) + 2)),x)

[Out]

6^(8*x)*exp(exp(2*x)*exp(exp(x)))

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sympy [A]  time = 0.27, size = 15, normalized size = 0.88 \begin {gather*} e^{8 x \log {\relax (6 )} + e^{2 x + e^{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x)+2)*exp(exp(x)+2*x)+8*ln(6))*exp(exp(exp(x)+2*x)+8*x*ln(6)),x)

[Out]

exp(8*x*log(6) + exp(2*x + exp(x)))

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