3.49.23 \(\int \frac {e^{-\frac {36 x^2-12 x^2 \log (\frac {5}{x})+x^2 \log ^2(\frac {5}{x})+(108 x-30 x \log (\frac {5}{x})+2 x \log ^2(\frac {5}{x})) \log (x)+(81-18 \log (\frac {5}{x})+\log ^2(\frac {5}{x})) \log ^2(x)}{x^2}} (-216 x-22 x^2+(60 x+4 x^2) \log (\frac {5}{x})-4 x \log ^2(\frac {5}{x})+(-324+156 x+(72-52 x) \log (\frac {5}{x})+(-4+4 x) \log ^2(\frac {5}{x})) \log (x)+(288-68 \log (\frac {5}{x})+4 \log ^2(\frac {5}{x})) \log ^2(x))}{x^2} \, dx\)

Optimal. Leaf size=32 \[ 2 e^{-\left (-3+\frac {\left (9-\log \left (\frac {5}{x}\right )\right ) (x+\log (x))}{x}\right )^2} x+\log (2) \]

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Rubi [F]  time = 56.31, 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 (-\frac {36 x^2-12 x^2 \log \left (\frac {5}{x}\right )+x^2 \log ^2\left (\frac {5}{x}\right )+\left (108 x-30 x \log \left (\frac {5}{x}\right )+2 x \log ^2\left (\frac {5}{x}\right )\right ) \log (x)+\left (81-18 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right ) \log ^2(x)}{x^2}\right ) \left (-216 x-22 x^2+\left (60 x+4 x^2\right ) \log \left (\frac {5}{x}\right )-4 x \log ^2\left (\frac {5}{x}\right )+\left (-324+156 x+(72-52 x) \log \left (\frac {5}{x}\right )+(-4+4 x) \log ^2\left (\frac {5}{x}\right )\right ) \log (x)+\left (288-68 \log \left (\frac {5}{x}\right )+4 \log ^2\left (\frac {5}{x}\right )\right ) \log ^2(x)\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-216*x - 22*x^2 + (60*x + 4*x^2)*Log[5/x] - 4*x*Log[5/x]^2 + (-324 + 156*x + (72 - 52*x)*Log[5/x] + (-4 +
4*x)*Log[5/x]^2)*Log[x] + (288 - 68*Log[5/x] + 4*Log[5/x]^2)*Log[x]^2)/(E^((36*x^2 - 12*x^2*Log[5/x] + x^2*Lo
g[5/x]^2 + (108*x - 30*x*Log[5/x] + 2*x*Log[5/x]^2)*Log[x] + (81 - 18*Log[5/x] + Log[5/x]^2)*Log[x]^2)/x^2)*x^
2),x]

[Out]

-5371093750*Defer[Int][E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)/x^((2*(54 + 6*x - 15*Log[5/x] +
Log[5/x]^2))/x), x] - 52734375000*Defer[Int][E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*x^(1 - (
2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x), x] + 976562500*Defer[Int][(E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])
^2*Log[x]^2)/x^2)*Log[5/x])/x^((2*(54 + 6*x - 15*Log[5/x] + Log[5/x]^2))/x), x] + 14648437500*Defer[Int][E^(-3
6 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*x^(1 - (2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x)*Log[5/x
], x] - 976562500*Defer[Int][E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*x^(1 - (2*(54 + 7*x - 15*
Log[5/x] + Log[5/x]^2))/x)*Log[5/x]^2, x] - 79101562500*Defer[Int][(E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*L
og[x]^2)/x^2)*Log[x])/x^((2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x), x] + 38085937500*Defer[Int][E^(-36 - Lo
g[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*x^(1 - (2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x)*Log[x], x] +
17578125000*Defer[Int][(E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*Log[5/x]*Log[x])/x^((2*(54 + 7
*x - 15*Log[5/x] + Log[5/x]^2))/x), x] - 12695312500*Defer[Int][E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x
]^2)/x^2)*x^(1 - (2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x)*Log[5/x]*Log[x], x] - 976562500*Defer[Int][(E^(-
36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*Log[5/x]^2*Log[x])/x^((2*(54 + 7*x - 15*Log[5/x] + Log[5/x
]^2))/x), x] + 976562500*Defer[Int][E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*x^(1 - (2*(54 + 7*
x - 15*Log[5/x] + Log[5/x]^2))/x)*Log[5/x]^2*Log[x], x] + 70312500000*Defer[Int][(E^(-36 - Log[5/x]^2 - ((-9 +
Log[5/x])^2*Log[x]^2)/x^2)*Log[x]^2)/x^((2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x), x] - 16601562500*Defer[
Int][(E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*Log[5/x]*Log[x]^2)/x^((2*(54 + 7*x - 15*Log[5/x]
+ Log[5/x]^2))/x), x] + 976562500*Defer[Int][(E^(-36 - Log[5/x]^2 - ((-9 + Log[5/x])^2*Log[x]^2)/x^2)*Log[5/x
]^2*Log[x]^2)/x^((2*(54 + 7*x - 15*Log[5/x] + Log[5/x]^2))/x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int 488281250 \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \left (-x (108+11 x)+6 (-27+13 x) \log (x)+144 \log ^2(x)+2 \log ^2\left (\frac {5}{x}\right ) (-1+\log (x)) (x+\log (x))+2 \log \left (\frac {5}{x}\right ) \left (x (15+x)+(18-13 x) \log (x)-17 \log ^2(x)\right )\right ) \, dx\\ &=488281250 \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \left (-x (108+11 x)+6 (-27+13 x) \log (x)+144 \log ^2(x)+2 \log ^2\left (\frac {5}{x}\right ) (-1+\log (x)) (x+\log (x))+2 \log \left (\frac {5}{x}\right ) \left (x (15+x)+(18-13 x) \log (x)-17 \log ^2(x)\right )\right ) \, dx\\ &=488281250 \int \left (-\exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{1-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} (108+11 x)+6 \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} (-27+13 x) \log (x)+144 \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log ^2(x)+2 \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log ^2\left (\frac {5}{x}\right ) (-1+\log (x)) (x+\log (x))+2 \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log \left (\frac {5}{x}\right ) \left (15 x+x^2+18 \log (x)-13 x \log (x)-17 \log ^2(x)\right )\right ) \, dx\\ &=-\left (488281250 \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{1-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} (108+11 x) \, dx\right )[phone] \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log ^2\left (\frac {5}{x}\right ) (-1+\log (x)) (x+\log (x)) \, dx+976562500 \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log \left (\frac {5}{x}\right ) \left (15 x+x^2+18 \log (x)-13 x \log (x)-17 \log ^2(x)\right ) \, dx+2929687500 \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} (-27+13 x) \log (x) \, dx+70312500000 \int \exp \left (-36-\log ^2\left (\frac {5}{x}\right )-\frac {\left (-9+\log \left (\frac {5}{x}\right )\right )^2 \log ^2(x)}{x^2}\right ) x^{-\frac {2 \left (54+7 x-15 \log \left (\frac {5}{x}\right )+\log ^2\left (\frac {5}{x}\right )\right )}{x}} \log ^2(x) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.60, size = 160, normalized size = 5.00 \begin {gather*} 2\ 5^{12+\frac {6 \left (5 x \log (x)+3 \left (\log \left (\frac {5}{x}\right )+\log (x)\right ) \left (9+\log \left (\frac {5}{x}\right )+\log (x)\right )\right )}{x^2}} e^{-\frac {18 \log ^3\left (\frac {5}{x}\right )+162 \log \left (\frac {5}{x}\right ) \log (x)+\log ^2\left (\frac {5}{x}\right ) \left (162+x^2+36 \log (x)+\log ^2(x)\right )+9 \left (4 x^2+9 \log ^2(x)\right )}{x^2}} \left (\frac {1}{x}\right )^{\frac {6 \left (5 x \log (x)+3 \left (\log \left (\frac {5}{x}\right )+\log (x)\right ) \left (9+\log \left (\frac {5}{x}\right )+\log (x)\right )\right )}{x^2}} x^{-\frac {108+11 x+2 \log ^2\left (\frac {5}{x}\right )}{x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-216*x - 22*x^2 + (60*x + 4*x^2)*Log[5/x] - 4*x*Log[5/x]^2 + (-324 + 156*x + (72 - 52*x)*Log[5/x] +
(-4 + 4*x)*Log[5/x]^2)*Log[x] + (288 - 68*Log[5/x] + 4*Log[5/x]^2)*Log[x]^2)/(E^((36*x^2 - 12*x^2*Log[5/x] +
x^2*Log[5/x]^2 + (108*x - 30*x*Log[5/x] + 2*x*Log[5/x]^2)*Log[x] + (81 - 18*Log[5/x] + Log[5/x]^2)*Log[x]^2)/x
^2)*x^2),x]

[Out]

(2*5^(12 + (6*(5*x*Log[x] + 3*(Log[5/x] + Log[x])*(9 + Log[5/x] + Log[x])))/x^2)*(x^(-1))^((6*(5*x*Log[x] + 3*
(Log[5/x] + Log[x])*(9 + Log[5/x] + Log[x])))/x^2))/(E^((18*Log[5/x]^3 + 162*Log[5/x]*Log[x] + Log[5/x]^2*(162
+ x^2 + 36*Log[x] + Log[x]^2) + 9*(4*x^2 + 9*Log[x]^2))/x^2)*x^((108 + 11*x + 2*Log[5/x]^2)/x))

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fricas [B]  time = 27.73, size = 110, normalized size = 3.44 \begin {gather*} 2 \, x e^{\left (\frac {2 \, {\left (x + \log \relax (5) + 9\right )} \log \left (\frac {5}{x}\right )^{3} - \log \left (\frac {5}{x}\right )^{4} - {\left (x^{2} + 2 \, {\left (x + 18\right )} \log \relax (5) + \log \relax (5)^{2} + 30 \, x + 81\right )} \log \left (\frac {5}{x}\right )^{2} - 36 \, x^{2} - 108 \, x \log \relax (5) - 81 \, \log \relax (5)^{2} + 6 \, {\left (2 \, x^{2} + {\left (5 \, x + 27\right )} \log \relax (5) + 3 \, \log \relax (5)^{2} + 18 \, x\right )} \log \left (\frac {5}{x}\right )}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*log(5/x)^2-68*log(5/x)+288)*log(x)^2+((4*x-4)*log(5/x)^2+(-52*x+72)*log(5/x)+156*x-324)*log(x)-4
*x*log(5/x)^2+(4*x^2+60*x)*log(5/x)-22*x^2-216*x)/x^2/exp(((log(5/x)^2-18*log(5/x)+81)*log(x)^2+(2*x*log(5/x)^
2-30*x*log(5/x)+108*x)*log(x)+x^2*log(5/x)^2-12*x^2*log(5/x)+36*x^2)/x^2),x, algorithm="fricas")

[Out]

2*x*e^((2*(x + log(5) + 9)*log(5/x)^3 - log(5/x)^4 - (x^2 + 2*(x + 18)*log(5) + log(5)^2 + 30*x + 81)*log(5/x)
^2 - 36*x^2 - 108*x*log(5) - 81*log(5)^2 + 6*(2*x^2 + (5*x + 27)*log(5) + 3*log(5)^2 + 18*x)*log(5/x))/x^2)

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giac [B]  time = 3.70, size = 139, normalized size = 4.34 \begin {gather*} 2 \, x e^{\left (-\frac {x^{2} \log \relax (5)^{2} - 2 \, x^{2} \log \relax (5) \log \relax (x) + 2 \, x \log \relax (5)^{2} \log \relax (x) + x^{2} \log \relax (x)^{2} - 4 \, x \log \relax (5) \log \relax (x)^{2} + \log \relax (5)^{2} \log \relax (x)^{2} + 2 \, x \log \relax (x)^{3} - 2 \, \log \relax (5) \log \relax (x)^{3} + \log \relax (x)^{4} - 12 \, x^{2} \log \relax (5) + 12 \, x^{2} \log \relax (x) - 30 \, x \log \relax (5) \log \relax (x) + 30 \, x \log \relax (x)^{2} - 18 \, \log \relax (5) \log \relax (x)^{2} + 18 \, \log \relax (x)^{3} + 36 \, x^{2} + 108 \, x \log \relax (x) + 81 \, \log \relax (x)^{2}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*log(5/x)^2-68*log(5/x)+288)*log(x)^2+((4*x-4)*log(5/x)^2+(-52*x+72)*log(5/x)+156*x-324)*log(x)-4
*x*log(5/x)^2+(4*x^2+60*x)*log(5/x)-22*x^2-216*x)/x^2/exp(((log(5/x)^2-18*log(5/x)+81)*log(x)^2+(2*x*log(5/x)^
2-30*x*log(5/x)+108*x)*log(x)+x^2*log(5/x)^2-12*x^2*log(5/x)+36*x^2)/x^2),x, algorithm="giac")

[Out]

2*x*e^(-(x^2*log(5)^2 - 2*x^2*log(5)*log(x) + 2*x*log(5)^2*log(x) + x^2*log(x)^2 - 4*x*log(5)*log(x)^2 + log(5
)^2*log(x)^2 + 2*x*log(x)^3 - 2*log(5)*log(x)^3 + log(x)^4 - 12*x^2*log(5) + 12*x^2*log(x) - 30*x*log(5)*log(x
) + 30*x*log(x)^2 - 18*log(5)*log(x)^2 + 18*log(x)^3 + 36*x^2 + 108*x*log(x) + 81*log(x)^2)/x^2)

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maple [A]  time = 1.17, size = 40, normalized size = 1.25

method	result	size
risch	\(2 x \,{\mathrm e}^{-\frac {\left (-\ln \relax (x )^{2}+\ln \relax (5) \ln \relax (x )-x \ln \relax (x )+x \ln \relax (5)-9 \ln \relax (x )-6 x \right )^{2}}{x^{2}}}\)	\(40\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*ln(5/x)^2-68*ln(5/x)+288)*ln(x)^2+((4*x-4)*ln(5/x)^2+(-52*x+72)*ln(5/x)+156*x-324)*ln(x)-4*x*ln(5/x)^2
+(4*x^2+60*x)*ln(5/x)-22*x^2-216*x)/x^2/exp(((ln(5/x)^2-18*ln(5/x)+81)*ln(x)^2+(2*x*ln(5/x)^2-30*x*ln(5/x)+108
*x)*ln(x)+x^2*ln(5/x)^2-12*x^2*ln(5/x)+36*x^2)/x^2),x,method=_RETURNVERBOSE)

[Out]

2*x*exp(-(-ln(x)^2+ln(5)*ln(x)-x*ln(x)+x*ln(5)-9*ln(x)-6*x)^2/x^2)

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maxima [B]  time = 0.79, size = 144, normalized size = 4.50 \begin {gather*} \frac {488281250 \, e^{\left (-\log \relax (5)^{2} + 2 \, \log \relax (5) \log \relax (x) - \frac {2 \, \log \relax (5)^{2} \log \relax (x)}{x} + \frac {4 \, \log \relax (5) \log \relax (x)^{2}}{x} - \frac {\log \relax (5)^{2} \log \relax (x)^{2}}{x^{2}} - \log \relax (x)^{2} - \frac {2 \, \log \relax (x)^{3}}{x} + \frac {2 \, \log \relax (5) \log \relax (x)^{3}}{x^{2}} - \frac {\log \relax (x)^{4}}{x^{2}} + \frac {30 \, \log \relax (5) \log \relax (x)}{x} - \frac {30 \, \log \relax (x)^{2}}{x} + \frac {18 \, \log \relax (5) \log \relax (x)^{2}}{x^{2}} - \frac {18 \, \log \relax (x)^{3}}{x^{2}} - \frac {108 \, \log \relax (x)}{x} - \frac {81 \, \log \relax (x)^{2}}{x^{2}} - 36\right )}}{x^{11}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*log(5/x)^2-68*log(5/x)+288)*log(x)^2+((4*x-4)*log(5/x)^2+(-52*x+72)*log(5/x)+156*x-324)*log(x)-4
*x*log(5/x)^2+(4*x^2+60*x)*log(5/x)-22*x^2-216*x)/x^2/exp(((log(5/x)^2-18*log(5/x)+81)*log(x)^2+(2*x*log(5/x)^
2-30*x*log(5/x)+108*x)*log(x)+x^2*log(5/x)^2-12*x^2*log(5/x)+36*x^2)/x^2),x, algorithm="maxima")

[Out]

488281250*e^(-log(5)^2 + 2*log(5)*log(x) - 2*log(5)^2*log(x)/x + 4*log(5)*log(x)^2/x - log(5)^2*log(x)^2/x^2 -
log(x)^2 - 2*log(x)^3/x + 2*log(5)*log(x)^3/x^2 - log(x)^4/x^2 + 30*log(5)*log(x)/x - 30*log(x)^2/x + 18*log(
5)*log(x)^2/x^2 - 18*log(x)^3/x^2 - 108*log(x)/x - 81*log(x)^2/x^2 - 36)/x^11

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mupad [B]  time = 4.26, size = 186, normalized size = 5.81 \begin {gather*} \frac {488281250\,5^{\frac {18\,{\ln \relax (x)}^2}{x^2}}\,x^{\frac {30\,\ln \left (\frac {1}{x}\right )}{x}}\,x^{\frac {30\,\ln \relax (5)}{x}}\,{\mathrm {e}}^{-36}\,{\mathrm {e}}^{-{\ln \left (\frac {1}{x}\right )}^2}\,{\mathrm {e}}^{-\frac {{\ln \left (\frac {1}{x}\right )}^2\,{\ln \relax (x)}^2}{x^2}}\,{\mathrm {e}}^{-{\ln \relax (5)}^2}\,{\mathrm {e}}^{-\frac {{\ln \relax (5)}^2\,{\ln \relax (x)}^2}{x^2}}\,{\mathrm {e}}^{-\frac {81\,{\ln \relax (x)}^2}{x^2}}\,{\left (\frac {1}{x}\right )}^{\frac {18\,{\ln \relax (x)}^2}{x^2}}}{x^{108/x}\,x^{\frac {2\,{\ln \left (\frac {1}{x}\right )}^2}{x}}\,x^{\frac {4\,\ln \left (\frac {1}{x}\right )\,\ln \relax (5)}{x}}\,x^{11}\,x^{\frac {2\,{\ln \relax (5)}^2}{x}}\,{\left (\frac {1}{x}\right )}^{2\,\ln \relax (5)}\,{\left (\frac {1}{x}\right )}^{\frac {2\,\ln \relax (5)\,{\ln \relax (x)}^2}{x^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(log(x)^2*(log(5/x)^2 - 18*log(5/x) + 81) + x^2*log(5/x)^2 + log(x)*(108*x - 30*x*log(5/x) + 2*x*lo
g(5/x)^2) + 36*x^2 - 12*x^2*log(5/x))/x^2)*(216*x - log(x)*(156*x - log(5/x)*(52*x - 72) + log(5/x)^2*(4*x - 4
) - 324) - log(x)^2*(4*log(5/x)^2 - 68*log(5/x) + 288) - log(5/x)*(60*x + 4*x^2) + 22*x^2 + 4*x*log(5/x)^2))/x
^2,x)

[Out]

(488281250*5^((18*log(x)^2)/x^2)*x^((30*log(1/x))/x)*x^((30*log(5))/x)*exp(-36)*exp(-log(1/x)^2)*exp(-(log(1/x
)^2*log(x)^2)/x^2)*exp(-log(5)^2)*exp(-(log(5)^2*log(x)^2)/x^2)*exp(-(81*log(x)^2)/x^2)*(1/x)^((18*log(x)^2)/x
^2))/(x^(108/x)*x^((2*log(1/x)^2)/x)*x^((4*log(1/x)*log(5))/x)*x^11*x^((2*log(5)^2)/x)*(1/x)^(2*log(5))*(1/x)^
((2*log(5)*log(x)^2)/x^2))

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sympy [B]  time = 1.65, size = 90, normalized size = 2.81 \begin {gather*} 2 x e^{- \frac {x^{2} \left (- \log {\relax (x )} + \log {\relax (5 )}\right )^{2} - 12 x^{2} \left (- \log {\relax (x )} + \log {\relax (5 )}\right ) + 36 x^{2} + \left (2 x \left (- \log {\relax (x )} + \log {\relax (5 )}\right )^{2} - 30 x \left (- \log {\relax (x )} + \log {\relax (5 )}\right ) + 108 x\right ) \log {\relax (x )} + \left (\left (- \log {\relax (x )} + \log {\relax (5 )}\right )^{2} + 18 \log {\relax (x )} - 18 \log {\relax (5 )} + 81\right ) \log {\relax (x )}^{2}}{x^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*ln(5/x)**2-68*ln(5/x)+288)*ln(x)**2+((4*x-4)*ln(5/x)**2+(-52*x+72)*ln(5/x)+156*x-324)*ln(x)-4*x*
ln(5/x)**2+(4*x**2+60*x)*ln(5/x)-22*x**2-216*x)/x**2/exp(((ln(5/x)**2-18*ln(5/x)+81)*ln(x)**2+(2*x*ln(5/x)**2-
30*x*ln(5/x)+108*x)*ln(x)+x**2*ln(5/x)**2-12*x**2*ln(5/x)+36*x**2)/x**2),x)

[Out]

2*x*exp(-(x**2*(-log(x) + log(5))**2 - 12*x**2*(-log(x) + log(5)) + 36*x**2 + (2*x*(-log(x) + log(5))**2 - 30*
x*(-log(x) + log(5)) + 108*x)*log(x) + ((-log(x) + log(5))**2 + 18*log(x) - 18*log(5) + 81)*log(x)**2)/x**2)

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