3.15.56 \(\int \frac {e^{\frac {-x+x \log (3)-4 x \log (\frac {25+6 x+5 \log (x)}{5+x+\log (x)})}{4 \log (\frac {25+6 x+5 \log (x)}{5+x+\log (x)})}} (4 x-4 x \log (3)+(x-x \log (3)) \log (x)+(-125-55 x-6 x^2+(125+55 x+6 x^2) \log (3)+(-50-11 x+(50+11 x) \log (3)) \log (x)+(-5+5 \log (3)) \log ^2(x)) \log (\frac {25+6 x+5 \log (x)}{5+x+\log (x)})+(-500-220 x-24 x^2+(-200-44 x) \log (x)-20 \log ^2(x)) \log ^2(\frac {25+6 x+5 \log (x)}{5+x+\log (x)}))}{(500+220 x+24 x^2+(200+44 x) \log (x)+20 \log ^2(x)) \log ^2(\frac {25+6 x+5 \log (x)}{5+x+\log (x)})} \, dx\)

Optimal. Leaf size=32 \[ e^{-x+\frac {-x+x \log (3)}{4 \log \left (5+\frac {x}{5+x+\log (x)}\right )}} \]

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Rubi [F]  time = 7.14, 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 {-x+x \log (3)-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \left (4 x-4 x \log (3)+(x-x \log (3)) \log (x)+\left (-125-55 x-6 x^2+\left (125+55 x+6 x^2\right ) \log (3)+(-50-11 x+(50+11 x) \log (3)) \log (x)+(-5+5 \log (3)) \log ^2(x)\right ) \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )+\left (-500-220 x-24 x^2+(-200-44 x) \log (x)-20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )\right )}{\left (500+220 x+24 x^2+(200+44 x) \log (x)+20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-x + x*Log[3] - 4*x*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])])/(4*Log[(25 + 6*x + 5*Log[x])/(5 + x
+ Log[x])]))*(4*x - 4*x*Log[3] + (x - x*Log[3])*Log[x] + (-125 - 55*x - 6*x^2 + (125 + 55*x + 6*x^2)*Log[3] +
(-50 - 11*x + (50 + 11*x)*Log[3])*Log[x] + (-5 + 5*Log[3])*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x]
)] + (-500 - 220*x - 24*x^2 + (-200 - 44*x)*Log[x] - 20*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]^
2))/((500 + 220*x + 24*x^2 + (200 + 44*x)*Log[x] + 20*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]^2)
,x]

[Out]

-Defer[Int][E^((x*(-4 + (-1 + Log[3])/Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]))/4), x] + (1 - Log[3])*Defe
r[Int][(E^((x*(-4 + (-1 + Log[3])/Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]))/4)*x)/((5 + x + Log[x])*(25 +
6*x + 5*Log[x])*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]^2), x] + ((1 - Log[3])*Defer[Int][(E^((x*(-4 + (-1
+ Log[3])/Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]))/4)*x*Log[x])/((5 + x + Log[x])*(25 + 6*x + 5*Log[x])*
Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]^2), x])/4 - ((1 - Log[3])*Defer[Int][E^((x*(-4 + (-1 + Log[3])/Log
[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]))/4)/Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])], x])/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-x+x \log (3)-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \left (x (4-4 \log (3))+(x-x \log (3)) \log (x)+\left (-125-55 x-6 x^2+\left (125+55 x+6 x^2\right ) \log (3)+(-50-11 x+(50+11 x) \log (3)) \log (x)+(-5+5 \log (3)) \log ^2(x)\right ) \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )+\left (-500-220 x-24 x^2+(-200-44 x) \log (x)-20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )\right )}{\left (500+220 x+24 x^2+(200+44 x) \log (x)+20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx\\ &=\int \frac {\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \left (x (4-4 \log (3))+(x-x \log (3)) \log (x)+\left (-125-55 x-6 x^2+\left (125+55 x+6 x^2\right ) \log (3)+(-50-11 x+(50+11 x) \log (3)) \log (x)+(-5+5 \log (3)) \log ^2(x)\right ) \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )+\left (-500-220 x-24 x^2+(-200-44 x) \log (x)-20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )\right )}{\left (500+220 x+24 x^2+(200+44 x) \log (x)+20 \log ^2(x)\right ) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx\\ &=\int \left (-\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )-\frac {\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) x (-1+\log (3)) (4+\log (x))}{4 (5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}+\frac {\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) (-1+\log (3))}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \, dx\\ &=\frac {1}{4} (1-\log (3)) \int \frac {\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) x (4+\log (x))}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx+\frac {1}{4} (-1+\log (3)) \int \frac {\exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx-\int \exp \left (\frac {-x (1-\log (3))-4 x \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \, dx\\ &=\frac {1}{4} (1-\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) x (4+\log (x))}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx+\frac {1}{4} (-1+\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right )}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx-\int \exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) \, dx\\ &=\frac {1}{4} (1-\log (3)) \int \left (\frac {4 \exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) x}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}+\frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) x \log (x)}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right ) \, dx+\frac {1}{4} (-1+\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right )}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx-\int \exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) \, dx\\ &=\frac {1}{4} (1-\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) x \log (x)}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx+(1-\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) x}{(5+x+\log (x)) (25+6 x+5 \log (x)) \log ^2\left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx+\frac {1}{4} (-1+\log (3)) \int \frac {\exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right )}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )} \, dx-\int \exp \left (\frac {1}{4} x \left (-4+\frac {-1+\log (3)}{\log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}\right )\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.35, size = 35, normalized size = 1.09 \begin {gather*} e^{-x+\frac {x (-1+\log (3))}{4 \log \left (\frac {25+6 x+5 \log (x)}{5+x+\log (x)}\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-x + x*Log[3] - 4*x*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])])/(4*Log[(25 + 6*x + 5*Log[x])/(
5 + x + Log[x])]))*(4*x - 4*x*Log[3] + (x - x*Log[3])*Log[x] + (-125 - 55*x - 6*x^2 + (125 + 55*x + 6*x^2)*Log
[3] + (-50 - 11*x + (50 + 11*x)*Log[3])*Log[x] + (-5 + 5*Log[3])*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x +
Log[x])] + (-500 - 220*x - 24*x^2 + (-200 - 44*x)*Log[x] - 20*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log
[x])]^2))/((500 + 220*x + 24*x^2 + (200 + 44*x)*Log[x] + 20*Log[x]^2)*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x
])]^2),x]

[Out]

E^(-x + (x*(-1 + Log[3]))/(4*Log[(25 + 6*x + 5*Log[x])/(5 + x + Log[x])]))

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fricas [A]  time = 0.80, size = 52, normalized size = 1.62 \begin {gather*} e^{\left (\frac {x \log \relax (3) - 4 \, x \log \left (\frac {6 \, x + 5 \, \log \relax (x) + 25}{x + \log \relax (x) + 5}\right ) - x}{4 \, \log \left (\frac {6 \, x + 5 \, \log \relax (x) + 25}{x + \log \relax (x) + 5}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*log(x)^2+(-44*x-200)*log(x)-24*x^2-220*x-500)*log((5*log(x)+6*x+25)/(5+log(x)+x))^2+((5*log(3)
-5)*log(x)^2+((11*x+50)*log(3)-11*x-50)*log(x)+(6*x^2+55*x+125)*log(3)-6*x^2-55*x-125)*log((5*log(x)+6*x+25)/(
5+log(x)+x))+(-x*log(3)+x)*log(x)-4*x*log(3)+4*x)*exp(1/4*(-4*x*log((5*log(x)+6*x+25)/(5+log(x)+x))+x*log(3)-x
)/log((5*log(x)+6*x+25)/(5+log(x)+x)))/(20*log(x)^2+(44*x+200)*log(x)+24*x^2+220*x+500)/log((5*log(x)+6*x+25)/
(5+log(x)+x))^2,x, algorithm="fricas")

[Out]

e^(1/4*(x*log(3) - 4*x*log((6*x + 5*log(x) + 25)/(x + log(x) + 5)) - x)/log((6*x + 5*log(x) + 25)/(x + log(x)
+ 5)))

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giac [B]  time = 9.96, size = 81, normalized size = 2.53 \begin {gather*} e^{\left (-x + \frac {x \log \relax (3)}{4 \, \log \left (\frac {6 \, x}{x + \log \relax (x) + 5} + \frac {5 \, \log \relax (x)}{x + \log \relax (x) + 5} + \frac {25}{x + \log \relax (x) + 5}\right )} - \frac {x}{4 \, \log \left (\frac {6 \, x}{x + \log \relax (x) + 5} + \frac {5 \, \log \relax (x)}{x + \log \relax (x) + 5} + \frac {25}{x + \log \relax (x) + 5}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*log(x)^2+(-44*x-200)*log(x)-24*x^2-220*x-500)*log((5*log(x)+6*x+25)/(5+log(x)+x))^2+((5*log(3)
-5)*log(x)^2+((11*x+50)*log(3)-11*x-50)*log(x)+(6*x^2+55*x+125)*log(3)-6*x^2-55*x-125)*log((5*log(x)+6*x+25)/(
5+log(x)+x))+(-x*log(3)+x)*log(x)-4*x*log(3)+4*x)*exp(1/4*(-4*x*log((5*log(x)+6*x+25)/(5+log(x)+x))+x*log(3)-x
)/log((5*log(x)+6*x+25)/(5+log(x)+x)))/(20*log(x)^2+(44*x+200)*log(x)+24*x^2+220*x+500)/log((5*log(x)+6*x+25)/
(5+log(x)+x))^2,x, algorithm="giac")

[Out]

e^(-x + 1/4*x*log(3)/log(6*x/(x + log(x) + 5) + 5*log(x)/(x + log(x) + 5) + 25/(x + log(x) + 5)) - 1/4*x/log(6
*x/(x + log(x) + 5) + 5*log(x)/(x + log(x) + 5) + 25/(x + log(x) + 5)))

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maple [C]  time = 47.45, size = 338, normalized size = 10.56

method	result	size
risch	\({\mathrm e}^{-\frac {x \left (-2 i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{3} \pi +2 i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{5+\ln \relax (x )+x}\right ) \pi +2 i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{2} \mathrm {csgn}\left (i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )\right ) \pi -2 i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right ) \mathrm {csgn}\left (\frac {i}{5+\ln \relax (x )+x}\right ) \mathrm {csgn}\left (i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )\right ) \pi +4 \ln \relax (2)+3 \ln \relax (3)-4 \ln \left (5+\ln \relax (x )+x \right )+4 \ln \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )+1\right )}{2 \left (-i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{3} \pi +i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{2} \mathrm {csgn}\left (\frac {i}{5+\ln \relax (x )+x}\right ) \pi +i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right )^{2} \mathrm {csgn}\left (i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )\right ) \pi -i \mathrm {csgn}\left (\frac {i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )}{5+\ln \relax (x )+x}\right ) \mathrm {csgn}\left (\frac {i}{5+\ln \relax (x )+x}\right ) \mathrm {csgn}\left (i \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )\right ) \pi +2 \ln \relax (2)+2 \ln \relax (3)-2 \ln \left (5+\ln \relax (x )+x \right )+2 \ln \left (\frac {5 \ln \relax (x )}{6}+x +\frac {25}{6}\right )\right )}}\)	\(338\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-20*ln(x)^2+(-44*x-200)*ln(x)-24*x^2-220*x-500)*ln((5*ln(x)+6*x+25)/(5+ln(x)+x))^2+((5*ln(3)-5)*ln(x)^2+
((11*x+50)*ln(3)-11*x-50)*ln(x)+(6*x^2+55*x+125)*ln(3)-6*x^2-55*x-125)*ln((5*ln(x)+6*x+25)/(5+ln(x)+x))+(-x*ln
(3)+x)*ln(x)-4*x*ln(3)+4*x)*exp(1/4*(-4*x*ln((5*ln(x)+6*x+25)/(5+ln(x)+x))+x*ln(3)-x)/ln((5*ln(x)+6*x+25)/(5+l
n(x)+x)))/(20*ln(x)^2+(44*x+200)*ln(x)+24*x^2+220*x+500)/ln((5*ln(x)+6*x+25)/(5+ln(x)+x))^2,x,method=_RETURNVE
RBOSE)

[Out]

exp(-1/2*x*(-2*I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))^3*Pi+2*I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))^2*csgn
(I/(5+ln(x)+x))*Pi+2*I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))^2*csgn(I*(5/6*ln(x)+x+25/6))*Pi-2*I*csgn(I/(5+ln
(x)+x)*(5/6*ln(x)+x+25/6))*csgn(I/(5+ln(x)+x))*csgn(I*(5/6*ln(x)+x+25/6))*Pi+4*ln(2)+3*ln(3)-4*ln(5+ln(x)+x)+4
*ln(5/6*ln(x)+x+25/6)+1)/(-I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))^3*Pi+I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/
6))^2*csgn(I/(5+ln(x)+x))*Pi+I*csgn(I/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))^2*csgn(I*(5/6*ln(x)+x+25/6))*Pi-I*csgn(I
/(5+ln(x)+x)*(5/6*ln(x)+x+25/6))*csgn(I/(5+ln(x)+x))*csgn(I*(5/6*ln(x)+x+25/6))*Pi+2*ln(2)+2*ln(3)-2*ln(5+ln(x
)+x)+2*ln(5/6*ln(x)+x+25/6)))

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*log(x)^2+(-44*x-200)*log(x)-24*x^2-220*x-500)*log((5*log(x)+6*x+25)/(5+log(x)+x))^2+((5*log(3)
-5)*log(x)^2+((11*x+50)*log(3)-11*x-50)*log(x)+(6*x^2+55*x+125)*log(3)-6*x^2-55*x-125)*log((5*log(x)+6*x+25)/(
5+log(x)+x))+(-x*log(3)+x)*log(x)-4*x*log(3)+4*x)*exp(1/4*(-4*x*log((5*log(x)+6*x+25)/(5+log(x)+x))+x*log(3)-x
)/log((5*log(x)+6*x+25)/(5+log(x)+x)))/(20*log(x)^2+(44*x+200)*log(x)+24*x^2+220*x+500)/log((5*log(x)+6*x+25)/
(5+log(x)+x))^2,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [B]  time = 2.50, size = 55, normalized size = 1.72 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{\frac {x\,\ln \relax (3)}{4\,\ln \left (\frac {6\,x+5\,\ln \relax (x)+25}{x+\ln \relax (x)+5}\right )}}\,{\mathrm {e}}^{-\frac {x}{4\,\ln \left (\frac {6\,x+5\,\ln \relax (x)+25}{x+\ln \relax (x)+5}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(x/4 + x*log((6*x + 5*log(x) + 25)/(x + log(x) + 5)) - (x*log(3))/4)/log((6*x + 5*log(x) + 25)/(x +
log(x) + 5)))*(4*x*log(3) - 4*x - log(x)*(x - x*log(3)) + log((6*x + 5*log(x) + 25)/(x + log(x) + 5))^2*(220*
x + 20*log(x)^2 + log(x)*(44*x + 200) + 24*x^2 + 500) + log((6*x + 5*log(x) + 25)/(x + log(x) + 5))*(55*x - lo
g(3)*(55*x + 6*x^2 + 125) + log(x)*(11*x - log(3)*(11*x + 50) + 50) - log(x)^2*(5*log(3) - 5) + 6*x^2 + 125)))
/(log((6*x + 5*log(x) + 25)/(x + log(x) + 5))^2*(220*x + 20*log(x)^2 + log(x)*(44*x + 200) + 24*x^2 + 500)),x)

[Out]

exp(-x)*exp((x*log(3))/(4*log((6*x + 5*log(x) + 25)/(x + log(x) + 5))))*exp(-x/(4*log((6*x + 5*log(x) + 25)/(x
+ log(x) + 5))))

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sympy [B]  time = 10.47, size = 49, normalized size = 1.53 \begin {gather*} e^{\frac {- x \log {\left (\frac {6 x + 5 \log {\relax (x )} + 25}{x + \log {\relax (x )} + 5} \right )} - \frac {x}{4} + \frac {x \log {\relax (3 )}}{4}}{\log {\left (\frac {6 x + 5 \log {\relax (x )} + 25}{x + \log {\relax (x )} + 5} \right )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-20*ln(x)**2+(-44*x-200)*ln(x)-24*x**2-220*x-500)*ln((5*ln(x)+6*x+25)/(5+ln(x)+x))**2+((5*ln(3)-5)
*ln(x)**2+((11*x+50)*ln(3)-11*x-50)*ln(x)+(6*x**2+55*x+125)*ln(3)-6*x**2-55*x-125)*ln((5*ln(x)+6*x+25)/(5+ln(x
)+x))+(-x*ln(3)+x)*ln(x)-4*x*ln(3)+4*x)*exp(1/4*(-4*x*ln((5*ln(x)+6*x+25)/(5+ln(x)+x))+x*ln(3)-x)/ln((5*ln(x)+
6*x+25)/(5+ln(x)+x)))/(20*ln(x)**2+(44*x+200)*ln(x)+24*x**2+220*x+500)/ln((5*ln(x)+6*x+25)/(5+ln(x)+x))**2,x)

[Out]

exp((-x*log((6*x + 5*log(x) + 25)/(x + log(x) + 5)) - x/4 + x*log(3)/4)/log((6*x + 5*log(x) + 25)/(x + log(x)
+ 5)))

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