3.10.92 \(\int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} (-2 x^2-2 x^3+3 x^4+(2-2 x^2) \log (x)-\log ^2(x))}{x^2} \, dx\) [992]

Optimal. Leaf size=25 \[ e^{e^{11-x \left (x-\left (-x+\frac {\log (x)}{x}\right )^2\right )}} \]

[Out]

exp(exp(11-x*(x-(ln(x)/x-x)^2)))

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Rubi [F]
time = 6.88, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x)*(
-2*x^2 - 2*x^3 + 3*x^4 + (2 - 2*x^2)*Log[x] - Log[x]^2))/x^2,x]

[Out]

-2*Defer[Int][E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x
]^2)/x), x] - 2*Defer[Int][E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*L
og[x] + Log[x]^2)/x)*x, x] + 3*Defer[Int][E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3
+ x^4 - 2*x^2*Log[x] + Log[x]^2)/x)*x^2, x] - 2*Defer[Int][E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/
x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x)*Log[x], x] + 2*Defer[Int][(E^(E^((11*x - x^3 + x^4 - 2*x^
2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x)*Log[x])/x^2, x] - Defer[Int][(E^(E^(
(11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x)*Log[x]^2)/x^
2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right )-2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x+3 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2-\frac {2 \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2}-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2}\right ) \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \left (-1+x^2\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \left (\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)-\frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2}\right ) \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ &=-\left (2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \, dx\right )-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x \, dx-2 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x) \, dx+2 \int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log (x)}{x^2} \, dx+3 \int \exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) x^2 \, dx-\int \frac {\exp \left (e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}\right ) \log ^2(x)}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]
time = 0.35, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{e^{\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}}+\frac {11 x-x^3+x^4-2 x^2 \log (x)+\log ^2(x)}{x}} \left (-2 x^2-2 x^3+3 x^4+\left (2-2 x^2\right ) \log (x)-\log ^2(x)\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2
)/x)*(-2*x^2 - 2*x^3 + 3*x^4 + (2 - 2*x^2)*Log[x] - Log[x]^2))/x^2,x]

[Out]

Integrate[(E^(E^((11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2)/x) + (11*x - x^3 + x^4 - 2*x^2*Log[x] + Log[x]^2
)/x)*(-2*x^2 - 2*x^3 + 3*x^4 + (2 - 2*x^2)*Log[x] - Log[x]^2))/x^2, x]

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Maple [A]
time = 0.03, size = 29, normalized size = 1.16

method	result	size
risch	\({\mathrm e}^{x^{-2 x} {\mathrm e}^{\frac {x^{4}-x^{3}+\ln \left (x \right )^{2}+11 x}{x}}}\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-ln(x)^2+(-2*x^2+2)*ln(x)+3*x^4-2*x^3-2*x^2)*exp((ln(x)^2-2*x^2*ln(x)+x^4-x^3+11*x)/x)*exp(exp((ln(x)^2-2
*x^2*ln(x)+x^4-x^3+11*x)/x))/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(x^(-2*x)*exp((x^4-x^3+ln(x)^2+11*x)/x))

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Maxima [A]
time = 0.53, size = 25, normalized size = 1.00 \begin {gather*} e^{\left (e^{\left (x^{3} - x^{2} - 2 \, x \log \left (x\right ) + \frac {\log \left (x\right )^{2}}{x} + 11\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)^2+(-2*x^2+2)*log(x)+3*x^4-2*x^3-2*x^2)*exp((log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x)*exp(exp(
(log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x))/x^2,x, algorithm="maxima")

[Out]

e^(e^(x^3 - x^2 - 2*x*log(x) + log(x)^2/x + 11))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (21) = 42\).
time = 0.37, size = 87, normalized size = 3.48 \begin {gather*} e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + x e^{\left (\frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x}\right )} + \log \left (x\right )^{2} + 11 \, x}{x} - \frac {x^{4} - x^{3} - 2 \, x^{2} \log \left (x\right ) + \log \left (x\right )^{2} + 11 \, x}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)^2+(-2*x^2+2)*log(x)+3*x^4-2*x^3-2*x^2)*exp((log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x)*exp(exp(
(log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x))/x^2,x, algorithm="fricas")

[Out]

e^((x^4 - x^3 - 2*x^2*log(x) + x*e^((x^4 - x^3 - 2*x^2*log(x) + log(x)^2 + 11*x)/x) + log(x)^2 + 11*x)/x - (x^
4 - x^3 - 2*x^2*log(x) + log(x)^2 + 11*x)/x)

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Sympy [A]
time = 0.58, size = 27, normalized size = 1.08 \begin {gather*} e^{e^{\frac {x^{4} - x^{3} - 2 x^{2} \log {\left (x \right )} + 11 x + \log {\left (x \right )}^{2}}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-ln(x)**2+(-2*x**2+2)*ln(x)+3*x**4-2*x**3-2*x**2)*exp((ln(x)**2-2*x**2*ln(x)+x**4-x**3+11*x)/x)*exp
(exp((ln(x)**2-2*x**2*ln(x)+x**4-x**3+11*x)/x))/x**2,x)

[Out]

exp(exp((x**4 - x**3 - 2*x**2*log(x) + 11*x + log(x)**2)/x))

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(x)^2+(-2*x^2+2)*log(x)+3*x^4-2*x^3-2*x^2)*exp((log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x)*exp(exp(
(log(x)^2-2*x^2*log(x)+x^4-x^3+11*x)/x))/x^2,x, algorithm="giac")

[Out]

integrate((3*x^4 - 2*x^3 - 2*x^2 - 2*(x^2 - 1)*log(x) - log(x)^2)*e^((x^4 - x^3 - 2*x^2*log(x) + log(x)^2 + 11
*x)/x + e^((x^4 - x^3 - 2*x^2*log(x) + log(x)^2 + 11*x)/x))/x^2, x)

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Mupad [B]
time = 1.15, size = 30, normalized size = 1.20 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{11}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{\frac {{\ln \left (x\right )}^2}{x}}}{x^{2\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((11*x - 2*x^2*log(x) + log(x)^2 - x^3 + x^4)/x)*exp(exp((11*x - 2*x^2*log(x) + log(x)^2 - x^3 + x^4)
/x))*(log(x)^2 + 2*x^2 + 2*x^3 - 3*x^4 + log(x)*(2*x^2 - 2)))/x^2,x)

[Out]

exp((exp(x^3)*exp(11)*exp(-x^2)*exp(log(x)^2/x))/x^(2*x))

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