3.59.92 \(\int e^{2+e^x+x+4 x^3+4 x^4 \log (x)} (1+e^x+12 x^2+4 x^3+16 x^3 \log (x)) \, dx\)

Optimal. Leaf size=19 \[ e^{2+e^x+x+x^3 (4+4 x \log (x))} \]

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Rubi [A]  time = 0.65, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 1, number of rules used = 1, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6706} \begin {gather*} e^{4 x^3+x+e^x+2} x^{4 x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(2 + E^x + x + 4*x^3 + 4*x^4*Log[x])*(1 + E^x + 12*x^2 + 4*x^3 + 16*x^3*Log[x]),x]

[Out]

E^(2 + E^x + x + 4*x^3)*x^(4*x^4)

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} &=e^{2+e^x+x+4 x^3} x^{4 x^4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 21, normalized size = 1.11 \begin {gather*} e^{2+e^x+x+4 x^3} x^{4 x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(2 + E^x + x + 4*x^3 + 4*x^4*Log[x])*(1 + E^x + 12*x^2 + 4*x^3 + 16*x^3*Log[x]),x]

[Out]

E^(2 + E^x + x + 4*x^3)*x^(4*x^4)

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fricas [A]  time = 0.69, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \relax (x) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3*log(x)+exp(x)+4*x^3+12*x^2+1)*exp(4*x^4*log(x)+exp(x)+4*x^3+x+2),x, algorithm="fricas")

[Out]

e^(4*x^4*log(x) + 4*x^3 + x + e^x + 2)

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giac [A]  time = 0.14, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \relax (x) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3*log(x)+exp(x)+4*x^3+12*x^2+1)*exp(4*x^4*log(x)+exp(x)+4*x^3+x+2),x, algorithm="giac")

[Out]

e^(4*x^4*log(x) + 4*x^3 + x + e^x + 2)

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maple [A]  time = 0.02, size = 19, normalized size = 1.00

method	result	size
derivativedivides	\({\mathrm e}^{4 x^{4} \ln \relax (x )+{\mathrm e}^{x}+4 x^{3}+x +2}\)	\(19\)
default	\({\mathrm e}^{4 x^{4} \ln \relax (x )+{\mathrm e}^{x}+4 x^{3}+x +2}\)	\(19\)
risch	\(x^{4 x^{4}} {\mathrm e}^{2+{\mathrm e}^{x}+4 x^{3}+x}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x^3*ln(x)+exp(x)+4*x^3+12*x^2+1)*exp(4*x^4*ln(x)+exp(x)+4*x^3+x+2),x,method=_RETURNVERBOSE)

[Out]

exp(4*x^4*ln(x)+exp(x)+4*x^3+x+2)

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maxima [A]  time = 0.36, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (4 \, x^{4} \log \relax (x) + 4 \, x^{3} + x + e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x^3*log(x)+exp(x)+4*x^3+12*x^2+1)*exp(4*x^4*log(x)+exp(x)+4*x^3+x+2),x, algorithm="maxima")

[Out]

e^(4*x^4*log(x) + 4*x^3 + x + e^x + 2)

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mupad [B]  time = 4.08, size = 21, normalized size = 1.11 \begin {gather*} x^{4\,x^4}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{4\,x^3}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x + exp(x) + 4*x^4*log(x) + 4*x^3 + 2)*(exp(x) + 16*x^3*log(x) + 12*x^2 + 4*x^3 + 1),x)

[Out]

x^(4*x^4)*exp(exp(x))*exp(2)*exp(4*x^3)*exp(x)

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sympy [A]  time = 0.36, size = 20, normalized size = 1.05 \begin {gather*} e^{4 x^{4} \log {\relax (x )} + 4 x^{3} + x + e^{x} + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*x**3*ln(x)+exp(x)+4*x**3+12*x**2+1)*exp(4*x**4*ln(x)+exp(x)+4*x**3+x+2),x)

[Out]

exp(4*x**4*log(x) + 4*x**3 + x + exp(x) + 2)

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