3.63.91 \(\int \frac {e^{e^{-x+25 \log ^{18-12 x+2 x^2}(e^3 x)}-x+25 \log ^{18-12 x+2 x^2}(e^3 x)} (-x \log (e^3 x)+\log ^{18-12 x+2 x^2}(e^3 x) (450-300 x+50 x^2+(-300 x+100 x^2) \log (e^3 x) \log (\log (e^3 x))))}{x \log (e^3 x)} \, dx\)

Optimal. Leaf size=24 \[ e^{e^{-x+25 \log ^{2 (-3+x)^2}\left (e^3 x\right )}} \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^(-x + 25*Log[E^3*x]^(18 - 12*x + 2*x^2)) - x + 25*Log[E^3*x]^(18 - 12*x + 2*x^2))*(-(x*Log[E^3*x]) +
Log[E^3*x]^(18 - 12*x + 2*x^2)*(450 - 300*x + 50*x^2 + (-300*x + 100*x^2)*Log[E^3*x]*Log[Log[E^3*x]])))/(x*Lo
g[E^3*x]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.84, size = 22, normalized size = 0.92 \begin {gather*} e^{e^{-x+25 (3+\log (x))^{2 (-3+x)^2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^(-x + 25*Log[E^3*x]^(18 - 12*x + 2*x^2)) - x + 25*Log[E^3*x]^(18 - 12*x + 2*x^2))*(-(x*Log[E^3
*x]) + Log[E^3*x]^(18 - 12*x + 2*x^2)*(450 - 300*x + 50*x^2 + (-300*x + 100*x^2)*Log[E^3*x]*Log[Log[E^3*x]])))
/(x*Log[E^3*x]),x]

[Out]

E^E^(-x + 25*(3 + Log[x])^(2*(-3 + x)^2))

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fricas [A]  time = 0.65, size = 24, normalized size = 1.00 \begin {gather*} e^{\left (e^{\left (-x + 25 \, \log \left (x e^{3}\right )^{2 \, x^{2} - 12 \, x + 18}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-300*x)*log(x*exp(3))*log(log(x*exp(3)))+50*x^2-300*x+450)*exp((x^2-6*x+9)*log(log(x*exp(3
))))^2-x*log(x*exp(3)))*exp(25*exp((x^2-6*x+9)*log(log(x*exp(3))))^2-x)*exp(exp(25*exp((x^2-6*x+9)*log(log(x*e
xp(3))))^2-x))/x/log(x*exp(3)),x, algorithm="fricas")

[Out]

e^(e^(-x + 25*log(x*e^3)^(2*x^2 - 12*x + 18)))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-300*x)*log(x*exp(3))*log(log(x*exp(3)))+50*x^2-300*x+450)*exp((x^2-6*x+9)*log(log(x*exp(3
))))^2-x*log(x*exp(3)))*exp(25*exp((x^2-6*x+9)*log(log(x*exp(3))))^2-x)*exp(exp(25*exp((x^2-6*x+9)*log(log(x*e
xp(3))))^2-x))/x/log(x*exp(3)),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.12, size = 22, normalized size = 0.92

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{25 \ln \left (x \,{\mathrm e}^{3}\right )^{2 \left (x -3\right )^{2}}-x}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((100*x^2-300*x)*ln(x*exp(3))*ln(ln(x*exp(3)))+50*x^2-300*x+450)*exp((x^2-6*x+9)*ln(ln(x*exp(3))))^2-x*ln
(x*exp(3)))*exp(25*exp((x^2-6*x+9)*ln(ln(x*exp(3))))^2-x)*exp(exp(25*exp((x^2-6*x+9)*ln(ln(x*exp(3))))^2-x))/x
/ln(x*exp(3)),x,method=_RETURNVERBOSE)

[Out]

exp(exp(25*(ln(x*exp(3))^((x-3)^2))^2-x))

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maxima [B]  time = 50.07, size = 494, normalized size = 20.58 \begin {gather*} e^{\left (e^{\left (25 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{18} + 1350 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{17} + 34425 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{16} + 550800 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{15} + 6196500 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{14} + 52050600 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{13} + 338328900 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{12} + 1739977200 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{11} + 7177405950 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{10} + 23924686500 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{9} + 64596653550 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{8} + 140938153200 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{7} + 246641768100 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{6} + 341503986600 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{5} + 365897128500 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{4} + 292717702800 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{3} + 164653707825 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x)^{2} + 58113073350 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )} \log \relax (x) - x + 9685512225 \, e^{\left (2 \, x^{2} \log \left (\log \relax (x) + 3\right ) - 12 \, x \log \left (\log \relax (x) + 3\right )\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-300*x)*log(x*exp(3))*log(log(x*exp(3)))+50*x^2-300*x+450)*exp((x^2-6*x+9)*log(log(x*exp(3
))))^2-x*log(x*exp(3)))*exp(25*exp((x^2-6*x+9)*log(log(x*exp(3))))^2-x)*exp(exp(25*exp((x^2-6*x+9)*log(log(x*e
xp(3))))^2-x))/x/log(x*exp(3)),x, algorithm="maxima")

[Out]

e^(e^(25*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^18 + 1350*e^(2*x^2*log(log(x) + 3) - 12*x*log
(log(x) + 3))*log(x)^17 + 34425*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^16 + 550800*e^(2*x^2*l
og(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^15 + 6196500*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*lo
g(x)^14 + 52050600*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^13 + 338328900*e^(2*x^2*log(log(x)
+ 3) - 12*x*log(log(x) + 3))*log(x)^12 + 1739977200*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^11
+ 7177405950*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^10 + 23924686500*e^(2*x^2*log(log(x) + 3
) - 12*x*log(log(x) + 3))*log(x)^9 + 64596653550*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^8 + 1
40938153200*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^7 + 246641768100*e^(2*x^2*log(log(x) + 3)
- 12*x*log(log(x) + 3))*log(x)^6 + 341503986600*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^5 + 36
5897128500*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^4 + 292717702800*e^(2*x^2*log(log(x) + 3) -
12*x*log(log(x) + 3))*log(x)^3 + 164653707825*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x)^2 + 581
13073350*e^(2*x^2*log(log(x) + 3) - 12*x*log(log(x) + 3))*log(x) - x + 9685512225*e^(2*x^2*log(log(x) + 3) - 1
2*x*log(log(x) + 3))))

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mupad [B]  time = 4.84, size = 399, normalized size = 16.62 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{9685512225\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{25\,{\ln \relax (x)}^{18}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{1350\,{\ln \relax (x)}^{17}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{34425\,{\ln \relax (x)}^{16}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{550800\,{\ln \relax (x)}^{15}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{6196500\,{\ln \relax (x)}^{14}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{52050600\,{\ln \relax (x)}^{13}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{64596653550\,{\ln \relax (x)}^8\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{338328900\,{\ln \relax (x)}^{12}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{292717702800\,{\ln \relax (x)}^3\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{58113073350\,\ln \relax (x)\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{365897128500\,{\ln \relax (x)}^4\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{164653707825\,{\ln \relax (x)}^2\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{1739977200\,{\ln \relax (x)}^{11}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{246641768100\,{\ln \relax (x)}^6\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{341503986600\,{\ln \relax (x)}^5\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{23924686500\,{\ln \relax (x)}^9\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{7177405950\,{\ln \relax (x)}^{10}\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}\,{\mathrm {e}}^{140938153200\,{\ln \relax (x)}^7\,{\left (\ln \relax (x)+3\right )}^{2\,x^2-12\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(25*exp(2*log(log(x*exp(3)))*(x^2 - 6*x + 9)) - x))*exp(25*exp(2*log(log(x*exp(3)))*(x^2 - 6*x +
9)) - x)*(exp(2*log(log(x*exp(3)))*(x^2 - 6*x + 9))*(300*x - 50*x^2 + log(log(x*exp(3)))*log(x*exp(3))*(300*x
- 100*x^2) - 450) + x*log(x*exp(3))))/(x*log(x*exp(3))),x)

[Out]

exp(exp(9685512225*(log(x) + 3)^(2*x^2 - 12*x))*exp(25*log(x)^18*(log(x) + 3)^(2*x^2 - 12*x))*exp(1350*log(x)^
17*(log(x) + 3)^(2*x^2 - 12*x))*exp(34425*log(x)^16*(log(x) + 3)^(2*x^2 - 12*x))*exp(550800*log(x)^15*(log(x)
+ 3)^(2*x^2 - 12*x))*exp(6196500*log(x)^14*(log(x) + 3)^(2*x^2 - 12*x))*exp(52050600*log(x)^13*(log(x) + 3)^(2
*x^2 - 12*x))*exp(64596653550*log(x)^8*(log(x) + 3)^(2*x^2 - 12*x))*exp(338328900*log(x)^12*(log(x) + 3)^(2*x^
2 - 12*x))*exp(-x)*exp(292717702800*log(x)^3*(log(x) + 3)^(2*x^2 - 12*x))*exp(58113073350*log(x)*(log(x) + 3)^
(2*x^2 - 12*x))*exp(365897128500*log(x)^4*(log(x) + 3)^(2*x^2 - 12*x))*exp(164653707825*log(x)^2*(log(x) + 3)^
(2*x^2 - 12*x))*exp(1739977200*log(x)^11*(log(x) + 3)^(2*x^2 - 12*x))*exp(246641768100*log(x)^6*(log(x) + 3)^(
2*x^2 - 12*x))*exp(341503986600*log(x)^5*(log(x) + 3)^(2*x^2 - 12*x))*exp(23924686500*log(x)^9*(log(x) + 3)^(2
*x^2 - 12*x))*exp(7177405950*log(x)^10*(log(x) + 3)^(2*x^2 - 12*x))*exp(140938153200*log(x)^7*(log(x) + 3)^(2*
x^2 - 12*x)))

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x**2-300*x)*ln(x*exp(3))*ln(ln(x*exp(3)))+50*x**2-300*x+450)*exp((x**2-6*x+9)*ln(ln(x*exp(3))
))**2-x*ln(x*exp(3)))*exp(25*exp((x**2-6*x+9)*ln(ln(x*exp(3))))**2-x)*exp(exp(25*exp((x**2-6*x+9)*ln(ln(x*exp(
3))))**2-x))/x/ln(x*exp(3)),x)

[Out]

Timed out

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