3.14.79 \(\int \frac {e^{-\frac {1}{-x+(-15+9 x-3 \log (4)+e^x (5-3 x+\log (4))) \log (x)}} (-15+8 x-3 \log (4)+e^x (5-3 x+\log (4))+(9 x+e^x (2 x-3 x^2+x \log (4))) \log (x))}{x^3+(30 x^2-18 x^3+6 x^2 \log (4)+e^x (-10 x^2+6 x^3-2 x^2 \log (4))) \log (x)+(225 x-270 x^2+81 x^3+(90 x-54 x^2) \log (4)+9 x \log ^2(4)+e^x (-150 x+180 x^2-54 x^3+(-60 x+36 x^2) \log (4)-6 x \log ^2(4))+e^{2 x} (25 x-30 x^2+9 x^3+(10 x-6 x^2) \log (4)+x \log ^2(4))) \log ^2(x)} \, dx\)
Optimal. Leaf size=26 \[ e^{\frac {1}{x-\left (3-e^x\right ) (-5+3 x-\log (4)) \log (x)}} \]
________________________________________________________________________________________
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[(-15 + 8*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]) + (9*x + E^x*(2*x - 3*x^2 + x*Log[4]))*Log[x])/(E^(-x + (-1
5 + 9*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]))*Log[x])^(-1)*(x^3 + (30*x^2 - 18*x^3 + 6*x^2*Log[4] + E^x*(-10*x^
2 + 6*x^3 - 2*x^2*Log[4]))*Log[x] + (225*x - 270*x^2 + 81*x^3 + (90*x - 54*x^2)*Log[4] + 9*x*Log[4]^2 + E^x*(-
150*x + 180*x^2 - 54*x^3 + (-60*x + 36*x^2)*Log[4] - 6*x*Log[4]^2) + E^(2*x)*(25*x - 30*x^2 + 9*x^3 + (10*x -
6*x^2)*Log[4] + x*Log[4]^2))*Log[x]^2)),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [A] time = 0.25, size = 23, normalized size = 0.88 \begin {gather*} e^{\frac {1}{x+\left (-3+e^x\right ) (-5+3 x-\log (4)) \log (x)}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-15 + 8*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]) + (9*x + E^x*(2*x - 3*x^2 + x*Log[4]))*Log[x])/(E^(-x
+ (-15 + 9*x - 3*Log[4] + E^x*(5 - 3*x + Log[4]))*Log[x])^(-1)*(x^3 + (30*x^2 - 18*x^3 + 6*x^2*Log[4] + E^x*(
-10*x^2 + 6*x^3 - 2*x^2*Log[4]))*Log[x] + (225*x - 270*x^2 + 81*x^3 + (90*x - 54*x^2)*Log[4] + 9*x*Log[4]^2 +
E^x*(-150*x + 180*x^2 - 54*x^3 + (-60*x + 36*x^2)*Log[4] - 6*x*Log[4]^2) + E^(2*x)*(25*x - 30*x^2 + 9*x^3 + (1
0*x - 6*x^2)*Log[4] + x*Log[4]^2))*Log[x]^2)),x]
[Out]
E^(x + (-3 + E^x)*(-5 + 3*x - Log[4])*Log[x])^(-1)
________________________________________________________________________________________
fricas [A] time = 0.79, size = 29, normalized size = 1.12 \begin {gather*} e^{\left (\frac {1}{{\left ({\left (3 \, x - 2 \, \log \relax (2) - 5\right )} e^{x} - 9 \, x + 6 \, \log \relax (2) + 15\right )} \log \relax (x) + x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp(x)-6*log(2)+8*x-15)*exp(-1/(((2*log
(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)
^2+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*log(2)^2+2*(-54*x^2+90*x)*log(2)+8
1*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*log(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x,
algorithm="fricas")
[Out]
e^(1/(((3*x - 2*log(2) - 5)*e^x - 9*x + 6*log(2) + 15)*log(x) + x))
________________________________________________________________________________________
giac [A] time = 0.42, size = 41, normalized size = 1.58 \begin {gather*} e^{\left (\frac {1}{3 \, x e^{x} \log \relax (x) - 2 \, e^{x} \log \relax (2) \log \relax (x) - 9 \, x \log \relax (x) - 5 \, e^{x} \log \relax (x) + 6 \, \log \relax (2) \log \relax (x) + x + 15 \, \log \relax (x)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp(x)-6*log(2)+8*x-15)*exp(-1/(((2*log
(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)
^2+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*log(2)^2+2*(-54*x^2+90*x)*log(2)+8
1*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*log(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x,
algorithm="giac")
[Out]
e^(1/(3*x*e^x*log(x) - 2*e^x*log(2)*log(x) - 9*x*log(x) - 5*e^x*log(x) + 6*log(2)*log(x) + x + 15*log(x)))
________________________________________________________________________________________
maple [A] time = 0.07, size = 46, normalized size = 1.77
|
|
|
| method |
result |
size |
|
|
|
| risch |
\({\mathrm e}^{-\frac {1}{2 \ln \relax (x ) {\mathrm e}^{x} \ln \relax (2)-3 x \,{\mathrm e}^{x} \ln \relax (x )+5 \,{\mathrm e}^{x} \ln \relax (x )-6 \ln \relax (2) \ln \relax (x )+9 x \ln \relax (x )-15 \ln \relax (x )-x}}\) |
\(46\) |
|
|
|
| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((2*x*ln(2)-3*x^2+2*x)*exp(x)+9*x)*ln(x)+(2*ln(2)-3*x+5)*exp(x)-6*ln(2)+8*x-15)*exp(-1/(((2*ln(2)-3*x+5)*
exp(x)-6*ln(2)+9*x-15)*ln(x)-x))/(((4*x*ln(2)^2+2*(-6*x^2+10*x)*ln(2)+9*x^3-30*x^2+25*x)*exp(x)^2+(-24*x*ln(2)
^2+2*(36*x^2-60*x)*ln(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*ln(2)^2+2*(-54*x^2+90*x)*ln(2)+81*x^3-270*x^2+225*x
)*ln(x)^2+((-4*x^2*ln(2)+6*x^3-10*x^2)*exp(x)+12*x^2*ln(2)-18*x^3+30*x^2)*ln(x)+x^3),x,method=_RETURNVERBOSE)
[Out]
exp(-1/(2*ln(x)*exp(x)*ln(2)-3*x*exp(x)*ln(x)+5*exp(x)*ln(x)-6*ln(2)*ln(x)+9*x*ln(x)-15*ln(x)-x))
________________________________________________________________________________________
maxima [A] time = 0.89, size = 29, normalized size = 1.12 \begin {gather*} e^{\left (\frac {1}{{\left ({\left (3 \, x - 2 \, \log \relax (2) - 5\right )} e^{x} - 9 \, x + 6 \, \log \relax (2) + 15\right )} \log \relax (x) + x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((2*x*log(2)-3*x^2+2*x)*exp(x)+9*x)*log(x)+(2*log(2)-3*x+5)*exp(x)-6*log(2)+8*x-15)*exp(-1/(((2*log
(2)-3*x+5)*exp(x)-6*log(2)+9*x-15)*log(x)-x))/(((4*x*log(2)^2+2*(-6*x^2+10*x)*log(2)+9*x^3-30*x^2+25*x)*exp(x)
^2+(-24*x*log(2)^2+2*(36*x^2-60*x)*log(2)-54*x^3+180*x^2-150*x)*exp(x)+36*x*log(2)^2+2*(-54*x^2+90*x)*log(2)+8
1*x^3-270*x^2+225*x)*log(x)^2+((-4*x^2*log(2)+6*x^3-10*x^2)*exp(x)+12*x^2*log(2)-18*x^3+30*x^2)*log(x)+x^3),x,
algorithm="maxima")
[Out]
e^(1/(((3*x - 2*log(2) - 5)*e^x - 9*x + 6*log(2) + 15)*log(x) + x))
________________________________________________________________________________________
mupad [B] time = 2.74, size = 41, normalized size = 1.58 \begin {gather*} {\mathrm {e}}^{\frac {1}{x+15\,\ln \relax (x)-5\,{\mathrm {e}}^x\,\ln \relax (x)+6\,\ln \relax (2)\,\ln \relax (x)-9\,x\,\ln \relax (x)-2\,{\mathrm {e}}^x\,\ln \relax (2)\,\ln \relax (x)+3\,x\,{\mathrm {e}}^x\,\ln \relax (x)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(1/(x - log(x)*(9*x - 6*log(2) + exp(x)*(2*log(2) - 3*x + 5) - 15)))*(8*x - 6*log(2) + exp(x)*(2*log(2
) - 3*x + 5) + log(x)*(9*x + exp(x)*(2*x + 2*x*log(2) - 3*x^2)) - 15))/(log(x)^2*(225*x + exp(2*x)*(25*x + 2*l
og(2)*(10*x - 6*x^2) + 4*x*log(2)^2 - 30*x^2 + 9*x^3) + 2*log(2)*(90*x - 54*x^2) + 36*x*log(2)^2 - exp(x)*(150
*x + 2*log(2)*(60*x - 36*x^2) + 24*x*log(2)^2 - 180*x^2 + 54*x^3) - 270*x^2 + 81*x^3) + log(x)*(12*x^2*log(2)
- exp(x)*(4*x^2*log(2) + 10*x^2 - 6*x^3) + 30*x^2 - 18*x^3) + x^3),x)
[Out]
exp(1/(x + 15*log(x) - 5*exp(x)*log(x) + 6*log(2)*log(x) - 9*x*log(x) - 2*exp(x)*log(2)*log(x) + 3*x*exp(x)*lo
g(x)))
________________________________________________________________________________________
sympy [A] time = 37.98, size = 32, normalized size = 1.23 \begin {gather*} e^{- \frac {1}{- x + \left (9 x + \left (- 3 x + 2 \log {\relax (2 )} + 5\right ) e^{x} - 15 - 6 \log {\relax (2 )}\right ) \log {\relax (x )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((2*x*ln(2)-3*x**2+2*x)*exp(x)+9*x)*ln(x)+(2*ln(2)-3*x+5)*exp(x)-6*ln(2)+8*x-15)*exp(-1/(((2*ln(2)-
3*x+5)*exp(x)-6*ln(2)+9*x-15)*ln(x)-x))/(((4*x*ln(2)**2+2*(-6*x**2+10*x)*ln(2)+9*x**3-30*x**2+25*x)*exp(x)**2+
(-24*x*ln(2)**2+2*(36*x**2-60*x)*ln(2)-54*x**3+180*x**2-150*x)*exp(x)+36*x*ln(2)**2+2*(-54*x**2+90*x)*ln(2)+81
*x**3-270*x**2+225*x)*ln(x)**2+((-4*x**2*ln(2)+6*x**3-10*x**2)*exp(x)+12*x**2*ln(2)-18*x**3+30*x**2)*ln(x)+x**
3),x)
[Out]
exp(-1/(-x + (9*x + (-3*x + 2*log(2) + 5)*exp(x) - 15 - 6*log(2))*log(x)))
________________________________________________________________________________________