3.45.41 \(\int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+(25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)) \log ^2(x)}{x^2 \log ^2(x)}} (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+(-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)) \log ^3(x))}{x^3 \log ^3(x)} \, dx\)

Optimal. Leaf size=27 \[ e^{\left (6+\frac {5-x-\log (3)-\frac {12}{\log (x)}}{x}\right )^2}+x \]

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Rubi [F]  time = 37.44, 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 {x^3 \log ^3(x)+\exp \left (\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x^3*Log[x]^3 + E^((144 + (-120 - 120*x + 24*Log[3])*Log[x] + (25 + 50*x + 25*x^2 + (-10 - 10*x)*Log[3] +
Log[3]^2)*Log[x]^2)/(x^2*Log[x]^2))*(-288 + (-168 + 120*x - 24*Log[3])*Log[x] + (240 + 120*x - 48*Log[3])*Log[
x]^2 + (-50 - 50*x + (20 + 10*x)*Log[3] - 2*Log[3]^2)*Log[x]^3))/(x^3*Log[x]^3),x]

[Out]

x - 2*(5 - Log[3])^2*Defer[Int][E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*x^2*Log[x]^2 + 25*(1
+ Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2))/(3^((2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*x^3), x] - 10*(5
- Log[3])*Defer[Int][E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*x^2*Log[x]^2 + 25*(1 + Log[3]^2/
25)*Log[x]^2)/(x^2*Log[x]^2))/(3^((2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*x^2), x] - 32*Defer[Int][(3^
(2 - (2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*
x^2*Log[x]^2 + 25*(1 + Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2)))/(x^3*Log[x]^3), x] - 8*(7 + Log[3])*Defer[Int][
(3^(1 - (2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 +
25*x^2*Log[x]^2 + 25*(1 + Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2)))/(x^3*Log[x]^2), x] + 40*Defer[Int][(3^(1 - (
2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*x^2*Lo
g[x]^2 + 25*(1 + Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2)))/(x^2*Log[x]^2), x] + 8*(10 - Log[9])*Defer[Int][(3^(1
- (2*(-12 + 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*x^
2*Log[x]^2 + 25*(1 + Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2)))/(x^3*Log[x]), x] + 40*Defer[Int][(3^(1 - (2*(-12
+ 5*Log[x] + 5*x*Log[x]))/(x^2*Log[x]))*E^((144 - 120*Log[x] - 120*x*Log[x] + 50*x*Log[x]^2 + 25*x^2*Log[x]^2
+ 25*(1 + Log[3]^2/25)*Log[x]^2)/(x^2*Log[x]^2)))/(x^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {2\ 3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (25+\frac {50}{x}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120}{x^2 \log (x)}-\frac {120}{x \log (x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)}\right ) \, dx\\ &=x+2 \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (25+\frac {50}{x}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120}{x^2 \log (x)}-\frac {120}{x \log (x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=x+2 \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) \left (12-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)\right ) \left (-12-12 \log (x)+5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)\right )}{x^3 \log ^3(x)} \, dx\\ &=x+2 \int \left (\frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5+5 x-\log (3)) (-5+\log (3))}{x^3}-\frac {16\ 3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}+\frac {4\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7+5 x-\log (3))}{x^3 \log ^2(x)}+\frac {4\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10+5 x-\log (9))}{x^3 \log (x)}\right ) \, dx\\ &=x+8 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7+5 x-\log (3))}{x^3 \log ^2(x)} \, dx+8 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10+5 x-\log (9))}{x^3 \log (x)} \, dx-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+(2 (-5+\log (3))) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5+5 x-\log (3))}{x^3} \, dx\\ &=x+8 \int \left (\frac {5\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log ^2(x)}+\frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (-7-\log (3))}{x^3 \log ^2(x)}\right ) \, dx+8 \int \left (\frac {5\ 3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log (x)}+\frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (10-\log (9))}{x^3 \log (x)}\right ) \, dx-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+(2 (-5+\log (3))) \int \left (\frac {5\ 3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2}+\frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right ) (5-\log (3))}{x^3}\right ) \, dx\\ &=x-32 \int \frac {3^{2-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)} \, dx+40 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log ^2(x)} \, dx+40 \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2 \log (x)} \, dx-(10 (5-\log (3))) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^2} \, dx-\left (2 (5-\log (3))^2\right ) \int \frac {3^{-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3} \, dx-(8 (7+\log (3))) \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log ^2(x)} \, dx+(8 (10-\log (9))) \int \frac {3^{1-\frac {2 (-12+5 \log (x)+5 x \log (x))}{x^2 \log (x)}} \exp \left (\frac {144-120 \log (x)-120 x \log (x)+50 x \log ^2(x)+25 x^2 \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)}{x^2 \log ^2(x)}\right )}{x^3 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.39, size = 65, normalized size = 2.41 \begin {gather*} 3^{-\frac {10}{x^2}-\frac {10}{x}+\frac {24}{x^2 \log (x)}} e^{25+\frac {50}{x}+\frac {25+\log ^2(3)}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120 (1+x)}{x^2 \log (x)}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(x^3*Log[x]^3 + E^((144 + (-120 - 120*x + 24*Log[3])*Log[x] + (25 + 50*x + 25*x^2 + (-10 - 10*x)*Log
[3] + Log[3]^2)*Log[x]^2)/(x^2*Log[x]^2))*(-288 + (-168 + 120*x - 24*Log[3])*Log[x] + (240 + 120*x - 48*Log[3]
)*Log[x]^2 + (-50 - 50*x + (20 + 10*x)*Log[3] - 2*Log[3]^2)*Log[x]^3))/(x^3*Log[x]^3),x]

[Out]

3^(-10/x^2 - 10/x + 24/(x^2*Log[x]))*E^(25 + 50/x + (25 + Log[3]^2)/x^2 + 144/(x^2*Log[x]^2) - (120*(1 + x))/(
x^2*Log[x])) + x

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fricas [B]  time = 0.60, size = 52, normalized size = 1.93 \begin {gather*} x + e^{\left (\frac {{\left (25 \, x^{2} - 10 \, {\left (x + 1\right )} \log \relax (3) + \log \relax (3)^{2} + 50 \, x + 25\right )} \log \relax (x)^{2} - 24 \, {\left (5 \, x - \log \relax (3) + 5\right )} \log \relax (x) + 144}{x^{2} \log \relax (x)^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+120*x+240)*log(x)^2+(-24*log(3)+120*x-
168)*log(x)-288)*exp(((log(3)^2+(-10*x-10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x
^2/log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="fricas")

[Out]

x + e^(((25*x^2 - 10*(x + 1)*log(3) + log(3)^2 + 50*x + 25)*log(x)^2 - 24*(5*x - log(3) + 5)*log(x) + 144)/(x^
2*log(x)^2))

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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((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+120*x+240)*log(x)^2+(-24*log(3)+120*x-
168)*log(x)-288)*exp(((log(3)^2+(-10*x-10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x
^2/log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="giac")

[Out]

undef

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maple [A]  time = 0.12, size = 30, normalized size = 1.11

method	result	size
risch	\(x +{\mathrm e}^{\frac {\left (\ln \relax (3) \ln \relax (x )-5 x \ln \relax (x )-5 \ln \relax (x )+12\right )^{2}}{\ln \relax (x )^{2} x^{2}}}\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*ln(3)^2+(10*x+20)*ln(3)-50*x-50)*ln(x)^3+(-48*ln(3)+120*x+240)*ln(x)^2+(-24*ln(3)+120*x-168)*ln(x)-2
88)*exp(((ln(3)^2+(-10*x-10)*ln(3)+25*x^2+50*x+25)*ln(x)^2+(24*ln(3)-120*x-120)*ln(x)+144)/x^2/ln(x)^2)+x^3*ln
(x)^3)/x^3/ln(x)^3,x,method=_RETURNVERBOSE)

[Out]

x+exp((ln(3)*ln(x)-5*x*ln(x)-5*ln(x)+12)^2/ln(x)^2/x^2)

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maxima [B]  time = 0.67, size = 75, normalized size = 2.78 \begin {gather*} x + e^{\left (-\frac {10 \, \log \relax (3)}{x} + \frac {\log \relax (3)^{2}}{x^{2}} + \frac {50}{x} - \frac {10 \, \log \relax (3)}{x^{2}} + \frac {25}{x^{2}} - \frac {120}{x \log \relax (x)} + \frac {24 \, \log \relax (3)}{x^{2} \log \relax (x)} - \frac {120}{x^{2} \log \relax (x)} + \frac {144}{x^{2} \log \relax (x)^{2}} + 25\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+120*x+240)*log(x)^2+(-24*log(3)+120*x-
168)*log(x)-288)*exp(((log(3)^2+(-10*x-10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x
^2/log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="maxima")

[Out]

x + e^(-10*log(3)/x + log(3)^2/x^2 + 50/x - 10*log(3)/x^2 + 25/x^2 - 120/(x*log(x)) + 24*log(3)/(x^2*log(x)) -
120/(x^2*log(x)) + 144/(x^2*log(x)^2) + 25)

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mupad [B]  time = 3.67, size = 85, normalized size = 3.15 \begin {gather*} x+\frac {3^{\frac {24}{x^2\,\ln \relax (x)}}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{\frac {{\ln \relax (3)}^2}{x^2}}\,{\mathrm {e}}^{\frac {25}{x^2}}\,{\mathrm {e}}^{50/x}\,{\mathrm {e}}^{-\frac {120}{x\,\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {120}{x^2\,\ln \relax (x)}}\,{\mathrm {e}}^{\frac {144}{x^2\,{\ln \relax (x)}^2}}}{3^{10/x}\,3^{\frac {10}{x^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((log(x)^2*(50*x - log(3)*(10*x + 10) + log(3)^2 + 25*x^2 + 25) - log(x)*(120*x - 24*log(3) + 120) +
144)/(x^2*log(x)^2))*(log(x)^3*(50*x - log(3)*(10*x + 20) + 2*log(3)^2 + 50) + log(x)*(24*log(3) - 120*x + 168
) - log(x)^2*(120*x - 48*log(3) + 240) + 288) - x^3*log(x)^3)/(x^3*log(x)^3),x)

[Out]

x + (3^(24/(x^2*log(x)))*exp(25)*exp(log(3)^2/x^2)*exp(25/x^2)*exp(50/x)*exp(-120/(x*log(x)))*exp(-120/(x^2*lo
g(x)))*exp(144/(x^2*log(x)^2)))/(3^(10/x)*3^(10/x^2))

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sympy [B]  time = 0.83, size = 56, normalized size = 2.07 \begin {gather*} x + e^{\frac {\left (- 120 x - 120 + 24 \log {\relax (3 )}\right ) \log {\relax (x )} + \left (25 x^{2} + 50 x + \left (- 10 x - 10\right ) \log {\relax (3 )} + \log {\relax (3 )}^{2} + 25\right ) \log {\relax (x )}^{2} + 144}{x^{2} \log {\relax (x )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*ln(3)**2+(10*x+20)*ln(3)-50*x-50)*ln(x)**3+(-48*ln(3)+120*x+240)*ln(x)**2+(-24*ln(3)+120*x-168
)*ln(x)-288)*exp(((ln(3)**2+(-10*x-10)*ln(3)+25*x**2+50*x+25)*ln(x)**2+(24*ln(3)-120*x-120)*ln(x)+144)/x**2/ln
(x)**2)+x**3*ln(x)**3)/x**3/ln(x)**3,x)

[Out]

x + exp(((-120*x - 120 + 24*log(3))*log(x) + (25*x**2 + 50*x + (-10*x - 10)*log(3) + log(3)**2 + 25)*log(x)**2
+ 144)/(x**2*log(x)**2))

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