3.87.32 \(\int \frac {(-144 x+72 x^2-9 x^3) \log (3)+(-24 x^2+6 x^3) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {(12 x-3 x^2) \log (3)+(6-2 x+x^2 \log (3)) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {(12 x-3 x^2) \log (3)+(6-2 x+x^2 \log (3)) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} (72-42 x+6 x^2+(144 x-72 x^2+9 x^3) \log (3)+(-6 x+(24 x^2-6 x^3) \log (3)) \log (x)+(-6 x+x^3 \log (3)) \log ^2(x))}{(144 x-72 x^2+9 x^3) \log (3)+(24 x^2-6 x^3) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx\)
Optimal. Leaf size=35 \[ 5+e^{e^{x+\frac {2 (-3+x)}{\log (3) \left (-x+\frac {3 (-4+x)}{\log (x)}\right )}}}-x \]
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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[((-144*x + 72*x^2 - 9*x^3)*Log[3] + (-24*x^2 + 6*x^3)*Log[3]*Log[x] - x^3*Log[3]*Log[x]^2 + E^(E^(((12*x -
3*x^2)*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x])) + ((12*x - 3*x^2)*Log[3
] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x]))*(72 - 42*x + 6*x^2 + (144*x - 72*x^2
+ 9*x^3)*Log[3] + (-6*x + (24*x^2 - 6*x^3)*Log[3])*Log[x] + (-6*x + x^3*Log[3])*Log[x]^2))/((144*x - 72*x^2 +
9*x^3)*Log[3] + (24*x^2 - 6*x^3)*Log[3]*Log[x] + x^3*Log[3]*Log[x]^2),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [A] time = 1.11, size = 57, normalized size = 1.63 \begin {gather*} \frac {e^{e^{\frac {-3 (-4+x) x \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{\log (3) (12-3 x+x \log (x))}}} \log (3)-x \log (3)}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((-144*x + 72*x^2 - 9*x^3)*Log[3] + (-24*x^2 + 6*x^3)*Log[3]*Log[x] - x^3*Log[3]*Log[x]^2 + E^(E^(((
12*x - 3*x^2)*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x])) + ((12*x - 3*x^2)
*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x]))*(72 - 42*x + 6*x^2 + (144*x -
72*x^2 + 9*x^3)*Log[3] + (-6*x + (24*x^2 - 6*x^3)*Log[3])*Log[x] + (-6*x + x^3*Log[3])*Log[x]^2))/((144*x - 72
*x^2 + 9*x^3)*Log[3] + (24*x^2 - 6*x^3)*Log[3]*Log[x] + x^3*Log[3]*Log[x]^2),x]
[Out]
(E^E^((-3*(-4 + x)*x*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/(Log[3]*(12 - 3*x + x*Log[x])))*Log[3] - x*Log[3]
)/Log[3]
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fricas [B] time = 0.52, size = 203, normalized size = 5.80 \begin {gather*} -{\left (x e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \relax (3) - {\left (x^{2} \log \relax (3) - 2 \, x + 6\right )} \log \relax (x)}{x \log \relax (3) \log \relax (x) - 3 \, {\left (x - 4\right )} \log \relax (3)}\right )} - e^{\left (\frac {{\left (x \log \relax (3) \log \relax (x) - 3 \, {\left (x - 4\right )} \log \relax (3)\right )} e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \relax (3) - {\left (x^{2} \log \relax (3) - 2 \, x + 6\right )} \log \relax (x)}{x \log \relax (3) \log \relax (x) - 3 \, {\left (x - 4\right )} \log \relax (3)}\right )} - 3 \, {\left (x^{2} - 4 \, x\right )} \log \relax (3) + {\left (x^{2} \log \relax (3) - 2 \, x + 6\right )} \log \relax (x)}{x \log \relax (3) \log \relax (x) - 3 \, {\left (x - 4\right )} \log \relax (3)}\right )}\right )} e^{\left (\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \relax (3) - {\left (x^{2} \log \relax (3) - 2 \, x + 6\right )} \log \relax (x)}{x \log \relax (3) \log \relax (x) - 3 \, {\left (x - 4\right )} \log \relax (3)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+(9*x^3-72*x^2+144*x)*log(3)+6*x^2-42
*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*
log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3))))-x^3*log(3)*log(x)^2+(6*x^3-24*
x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x)*log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*
x^2+144*x)*log(3)),x, algorithm="fricas")
[Out]
-(x*e^(-(3*(x^2 - 4*x)*log(3) - (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) - 3*(x - 4)*log(3))) - e^(((x*
log(3)*log(x) - 3*(x - 4)*log(3))*e^(-(3*(x^2 - 4*x)*log(3) - (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x)
- 3*(x - 4)*log(3))) - 3*(x^2 - 4*x)*log(3) + (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) - 3*(x - 4)*log(
3))))*e^((3*(x^2 - 4*x)*log(3) - (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) - 3*(x - 4)*log(3)))
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+(9*x^3-72*x^2+144*x)*log(3)+6*x^2-42
*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*
log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3))))-x^3*log(3)*log(x)^2+(6*x^3-24*
x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x)*log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*
x^2+144*x)*log(3)),x, algorithm="giac")
[Out]
undef
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maple [A] time = 0.29, size = 53, normalized size = 1.51
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\(-x +{\mathrm e}^{{\mathrm e}^{\frac {x^{2} \ln \relax (3) \ln \relax (x )-3 x^{2} \ln \relax (3)-2 x \ln \relax (x )+12 x \ln \relax (3)+6 \ln \relax (x )}{\ln \relax (3) \left (x \ln \relax (x )-3 x +12\right )}}}\) |
\(53\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((x^3*ln(3)-6*x)*ln(x)^2+((-6*x^3+24*x^2)*ln(3)-6*x)*ln(x)+(9*x^3-72*x^2+144*x)*ln(3)+6*x^2-42*x+72)*exp(
((x^2*ln(3)+6-2*x)*ln(x)+(-3*x^2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3)))*exp(exp(((x^2*ln(3)+6-2*x)*ln(x
)+(-3*x^2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3))))-x^3*ln(3)*ln(x)^2+(6*x^3-24*x^2)*ln(3)*ln(x)+(-9*x^3+
72*x^2-144*x)*ln(3))/(x^3*ln(3)*ln(x)^2+(-6*x^3+24*x^2)*ln(3)*ln(x)+(9*x^3-72*x^2+144*x)*ln(3)),x,method=_RETU
RNVERBOSE)
[Out]
-x+exp(exp((x^2*ln(3)*ln(x)-3*x^2*ln(3)-2*x*ln(x)+12*x*ln(3)+6*ln(x))/ln(3)/(x*ln(x)-3*x+12)))
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maxima [B] time = 0.76, size = 264, normalized size = 7.54 \begin {gather*} -x + e^{\left (e^{\left (\frac {x \log \relax (x)^{2}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} - \frac {6 \, x \log \relax (x)}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} + \frac {9 \, x}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} + \frac {24 \, \log \relax (x)}{x \log \relax (3) \log \relax (x)^{2} + 9 \, x \log \relax (3) - 6 \, {\left (x \log \relax (3) - 2 \, \log \relax (3)\right )} \log \relax (x) - 36 \, \log \relax (3)} + \frac {144 \, \log \relax (x)}{x \log \relax (x)^{3} - 3 \, {\left (3 \, x - 4\right )} \log \relax (x)^{2} + 9 \, {\left (3 \, x - 8\right )} \log \relax (x) - 27 \, x + 108} + \frac {6 \, \log \relax (x)}{x \log \relax (3) \log \relax (x) - 3 \, x \log \relax (3) + 12 \, \log \relax (3)} - \frac {2 \, \log \relax (x)}{\log \relax (3) \log \relax (x) - 3 \, \log \relax (3)} - \frac {12 \, \log \relax (x)}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} - \frac {432}{x \log \relax (x)^{3} - 3 \, {\left (3 \, x - 4\right )} \log \relax (x)^{2} + 9 \, {\left (3 \, x - 8\right )} \log \relax (x) - 27 \, x + 108} - \frac {144}{x \log \relax (x)^{2} - 6 \, {\left (x - 2\right )} \log \relax (x) + 9 \, x - 36} + \frac {36}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9} + \frac {12}{\log \relax (x) - 3}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+(9*x^3-72*x^2+144*x)*log(3)+6*x^2-42
*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*
log(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3))))-x^3*log(3)*log(x)^2+(6*x^3-24*
x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x)*log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*
x^2+144*x)*log(3)),x, algorithm="maxima")
[Out]
-x + e^(e^(x*log(x)^2/(log(x)^2 - 6*log(x) + 9) - 6*x*log(x)/(log(x)^2 - 6*log(x) + 9) + 9*x/(log(x)^2 - 6*log
(x) + 9) + 24*log(x)/(x*log(3)*log(x)^2 + 9*x*log(3) - 6*(x*log(3) - 2*log(3))*log(x) - 36*log(3)) + 144*log(x
)/(x*log(x)^3 - 3*(3*x - 4)*log(x)^2 + 9*(3*x - 8)*log(x) - 27*x + 108) + 6*log(x)/(x*log(3)*log(x) - 3*x*log(
3) + 12*log(3)) - 2*log(x)/(log(3)*log(x) - 3*log(3)) - 12*log(x)/(log(x)^2 - 6*log(x) + 9) - 432/(x*log(x)^3
- 3*(3*x - 4)*log(x)^2 + 9*(3*x - 8)*log(x) - 27*x + 108) - 144/(x*log(x)^2 - 6*(x - 2)*log(x) + 9*x - 36) + 3
6/(log(x)^2 - 6*log(x) + 9) + 12/(log(x) - 3)))
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mupad [B] time = 7.53, size = 130, normalized size = 3.71 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {2\,x\,\ln \relax (x)}{12\,\ln \relax (3)-3\,x\,\ln \relax (3)+x\,\ln \relax (3)\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {6\,\ln \relax (x)}{12\,\ln \relax (3)-3\,x\,\ln \relax (3)+x\,\ln \relax (3)\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {12\,x\,\ln \relax (3)}{12\,\ln \relax (3)-3\,x\,\ln \relax (3)+x\,\ln \relax (3)\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {x^2\,\ln \relax (3)\,\ln \relax (x)}{12\,\ln \relax (3)-3\,x\,\ln \relax (3)+x\,\ln \relax (3)\,\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {3\,x^2\,\ln \relax (3)}{12\,\ln \relax (3)-3\,x\,\ln \relax (3)+x\,\ln \relax (3)\,\ln \relax (x)}}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(log(3)*(144*x - 72*x^2 + 9*x^3) + log(3)*log(x)*(24*x^2 - 6*x^3) + x^3*log(3)*log(x)^2 + exp(-(log(x)*(x
^2*log(3) - 2*x + 6) + log(3)*(12*x - 3*x^2))/(log(3)*(3*x - 12) - x*log(3)*log(x)))*exp(exp(-(log(x)*(x^2*log
(3) - 2*x + 6) + log(3)*(12*x - 3*x^2))/(log(3)*(3*x - 12) - x*log(3)*log(x))))*(42*x + log(x)*(6*x - log(3)*(
24*x^2 - 6*x^3)) - log(3)*(144*x - 72*x^2 + 9*x^3) + log(x)^2*(6*x - x^3*log(3)) - 6*x^2 - 72))/(log(3)*(144*x
- 72*x^2 + 9*x^3) + log(3)*log(x)*(24*x^2 - 6*x^3) + x^3*log(3)*log(x)^2),x)
[Out]
exp(exp(-(2*x*log(x))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))*exp((6*log(x))/(12*log(3) - 3*x*log(3) + x*l
og(3)*log(x)))*exp((12*x*log(3))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))*exp((x^2*log(3)*log(x))/(12*log(3
) - 3*x*log(3) + x*log(3)*log(x)))*exp(-(3*x^2*log(3))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))) - x
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sympy [A] time = 6.01, size = 48, normalized size = 1.37 \begin {gather*} - x + e^{e^{\frac {\left (- 3 x^{2} + 12 x\right ) \log {\relax (3 )} + \left (x^{2} \log {\relax (3 )} - 2 x + 6\right ) \log {\relax (x )}}{x \log {\relax (3 )} \log {\relax (x )} + \left (12 - 3 x\right ) \log {\relax (3 )}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((x**3*ln(3)-6*x)*ln(x)**2+((-6*x**3+24*x**2)*ln(3)-6*x)*ln(x)+(9*x**3-72*x**2+144*x)*ln(3)+6*x**2-
42*x+72)*exp(((x**2*ln(3)+6-2*x)*ln(x)+(-3*x**2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3)))*exp(exp(((x**2*l
n(3)+6-2*x)*ln(x)+(-3*x**2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3))))-x**3*ln(3)*ln(x)**2+(6*x**3-24*x**2)
*ln(3)*ln(x)+(-9*x**3+72*x**2-144*x)*ln(3))/(x**3*ln(3)*ln(x)**2+(-6*x**3+24*x**2)*ln(3)*ln(x)+(9*x**3-72*x**2
+144*x)*ln(3)),x)
[Out]
-x + exp(exp(((-3*x**2 + 12*x)*log(3) + (x**2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) + (12 - 3*x)*log(3)))
)
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