3.49.10 \(\int \frac {-16 x+4 x^2-4 x^3-4 e^x x^4-9 x^6+(16+4 e^x x^3+9 x^5) \log (x)+(8 x^3-2 x^4+2 x^5+2 e^x x^6+(-8 x^2-2 e^x x^5) \log (x)) \log (e^{e^8+e^x} (x-\log (x)))}{-9 x^6+9 x^5 \log (x)} \, dx\)

Optimal. Leaf size=33 \[ x-\frac {1}{9} \left (\frac {2}{x^2}-\log \left (e^{e^8+e^x} (x-\log (x))\right )\right )^2 \]

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Rubi [F]  time = 3.70, 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 {-16 x+4 x^2-4 x^3-4 e^x x^4-9 x^6+\left (16+4 e^x x^3+9 x^5\right ) \log (x)+\left (8 x^3-2 x^4+2 x^5+2 e^x x^6+\left (-8 x^2-2 e^x x^5\right ) \log (x)\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{-9 x^6+9 x^5 \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-16*x + 4*x^2 - 4*x^3 - 4*E^x*x^4 - 9*x^6 + (16 + 4*E^x*x^3 + 9*x^5)*Log[x] + (8*x^3 - 2*x^4 + 2*x^5 + 2*
E^x*x^6 + (-8*x^2 - 2*E^x*x^5)*Log[x])*Log[E^(E^8 + E^x)*(x - Log[x])])/(-9*x^6 + 9*x^5*Log[x]),x]

[Out]

E^(2*x)/9 - 4/(9*x^4) - (4*E^x)/(9*x) + x + (4*ExpIntegralEi[x])/9 - (2*E^x*Log[E^(E^8 + E^x)*(x - Log[x])])/9
+ (2*Defer[Int][E^x/(x - Log[x]), x])/9 - (4*Defer[Int][1/(x^3*(x - Log[x])), x])/9 + (4*Defer[Int][1/(x^2*(x
- Log[x])), x])/9 - (2*Defer[Int][E^x/(x*(x - Log[x])), x])/9 - (2*Defer[Int][Log[E^(E^8 + E^x)*(x - Log[x])]
/(x - Log[x]), x])/9 - (8*Defer[Int][Log[E^(E^8 + E^x)*(x - Log[x])]/(x^2*(x - Log[x])), x])/9 + (2*Defer[Int]
[Log[E^(E^8 + E^x)*(x - Log[x])]/(x*(x - Log[x])), x])/9 + (8*Defer[Int][(Log[x]*Log[E^(E^8 + E^x)*(x - Log[x]
)])/(x^3*(x - Log[x])), x])/9

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16 x+4 x^2-4 x^3-4 e^x x^4-9 x^6+\left (16+4 e^x x^3+9 x^5\right ) \log (x)+\left (8 x^3-2 x^4+2 x^5+2 e^x x^6+\left (-8 x^2-2 e^x x^5\right ) \log (x)\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^5 (-9 x+9 \log (x))} \, dx\\ &=\int \frac {16 x-4 x^2+4 x^3+4 e^x x^4+9 x^6-\left (16+4 e^x x^3+9 x^5\right ) \log (x)-\left (8 x^3-2 x^4+2 x^5+2 e^x x^6+\left (-8 x^2-2 e^x x^5\right ) \log (x)\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{9 x^5 (x-\log (x))} \, dx\\ &=\frac {1}{9} \int \frac {16 x-4 x^2+4 x^3+4 e^x x^4+9 x^6-\left (16+4 e^x x^3+9 x^5\right ) \log (x)-\left (8 x^3-2 x^4+2 x^5+2 e^x x^6+\left (-8 x^2-2 e^x x^5\right ) \log (x)\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^5 (x-\log (x))} \, dx\\ &=\frac {1}{9} \int \left (\frac {16}{x^4 (x-\log (x))}-\frac {4}{x^3 (x-\log (x))}+\frac {4}{x^2 (x-\log (x))}+\frac {9 x}{x-\log (x)}-\frac {9 \log (x)}{x-\log (x)}-\frac {16 \log (x)}{x^5 (x-\log (x))}-\frac {2 \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)}-\frac {8 \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))}+\frac {2 \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))}+\frac {8 \log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))}-\frac {2 e^x \left (-2+x^2 \log \left (e^{e^8+e^x} (x-\log (x))\right )\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx\right )+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {2}{9} \int \frac {e^x \left (-2+x^2 \log \left (e^{e^8+e^x} (x-\log (x))\right )\right )}{x^2} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx+\frac {16}{9} \int \frac {1}{x^4 (x-\log (x))} \, dx-\frac {16}{9} \int \frac {\log (x)}{x^5 (x-\log (x))} \, dx+\int \frac {x}{x-\log (x)} \, dx-\int \frac {\log (x)}{x-\log (x)} \, dx\\ &=-\left (\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx\right )+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {2}{9} \int \left (-\frac {2 e^x}{x^2}+e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )\right ) \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx-\frac {16}{9} \int \left (-\frac {1}{x^5}+\frac {1}{x^4 (x-\log (x))}\right ) \, dx+\frac {16}{9} \int \frac {1}{x^4 (x-\log (x))} \, dx-\int \left (-1+\frac {x}{x-\log (x)}\right ) \, dx+\int \frac {x}{x-\log (x)} \, dx\\ &=-\frac {4}{9 x^4}+x-\frac {2}{9} \int e^x \log \left (e^{e^8+e^x} (x-\log (x))\right ) \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx+\frac {4}{9} \int \frac {e^x}{x^2} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ &=-\frac {4}{9 x^4}-\frac {4 e^x}{9 x}+x-\frac {2}{9} e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )+\frac {2}{9} \int \frac {e^x \left (-1+x+e^x x^2-e^x x \log (x)\right )}{x (x-\log (x))} \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx+\frac {4}{9} \int \frac {e^x}{x} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ &=-\frac {4}{9 x^4}-\frac {4 e^x}{9 x}+x+\frac {4 \text {Ei}(x)}{9}-\frac {2}{9} e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )+\frac {2}{9} \int \left (e^{2 x}+\frac {e^x (-1+x)}{x (x-\log (x))}\right ) \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ &=-\frac {4}{9 x^4}-\frac {4 e^x}{9 x}+x+\frac {4 \text {Ei}(x)}{9}-\frac {2}{9} e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )+\frac {2}{9} \int e^{2 x} \, dx+\frac {2}{9} \int \frac {e^x (-1+x)}{x (x-\log (x))} \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ &=\frac {e^{2 x}}{9}-\frac {4}{9 x^4}-\frac {4 e^x}{9 x}+x+\frac {4 \text {Ei}(x)}{9}-\frac {2}{9} e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )+\frac {2}{9} \int \left (\frac {e^x}{x-\log (x)}-\frac {e^x}{x (x-\log (x))}\right ) \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ &=\frac {e^{2 x}}{9}-\frac {4}{9 x^4}-\frac {4 e^x}{9 x}+x+\frac {4 \text {Ei}(x)}{9}-\frac {2}{9} e^x \log \left (e^{e^8+e^x} (x-\log (x))\right )+\frac {2}{9} \int \frac {e^x}{x-\log (x)} \, dx-\frac {2}{9} \int \frac {e^x}{x (x-\log (x))} \, dx-\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x-\log (x)} \, dx+\frac {2}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x (x-\log (x))} \, dx-\frac {4}{9} \int \frac {1}{x^3 (x-\log (x))} \, dx+\frac {4}{9} \int \frac {1}{x^2 (x-\log (x))} \, dx-\frac {8}{9} \int \frac {\log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^2 (x-\log (x))} \, dx+\frac {8}{9} \int \frac {\log (x) \log \left (e^{e^8+e^x} (x-\log (x))\right )}{x^3 (x-\log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.26, size = 88, normalized size = 2.67 \begin {gather*} \frac {1}{9} \left (e^{2 x}-\frac {4}{x^4}+9 x+\log ^2(x-\log (x))+2 \log (x-\log (x)) \left (e^x-\log \left (e^{e^8+e^x} (x-\log (x))\right )\right )+\left (-2 e^x+\frac {4}{x^2}\right ) \log \left (e^{e^8+e^x} (x-\log (x))\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16*x + 4*x^2 - 4*x^3 - 4*E^x*x^4 - 9*x^6 + (16 + 4*E^x*x^3 + 9*x^5)*Log[x] + (8*x^3 - 2*x^4 + 2*x^
5 + 2*E^x*x^6 + (-8*x^2 - 2*E^x*x^5)*Log[x])*Log[E^(E^8 + E^x)*(x - Log[x])])/(-9*x^6 + 9*x^5*Log[x]),x]

[Out]

(E^(2*x) - 4/x^4 + 9*x + Log[x - Log[x]]^2 + 2*Log[x - Log[x]]*(E^x - Log[E^(E^8 + E^x)*(x - Log[x])]) + (-2*E
^x + 4/x^2)*Log[E^(E^8 + E^x)*(x - Log[x])])/9

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fricas [A]  time = 1.02, size = 51, normalized size = 1.55 \begin {gather*} -\frac {x^{4} \log \left ({\left (x - \log \relax (x)\right )} e^{\left (e^{8} + e^{x}\right )}\right )^{2} - 9 \, x^{5} - 4 \, x^{2} \log \left ({\left (x - \log \relax (x)\right )} e^{\left (e^{8} + e^{x}\right )}\right ) + 4}{9 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^5*exp(x)-8*x^2)*log(x)+2*x^6*exp(x)+2*x^5-2*x^4+8*x^3)*log((x-log(x))*exp(exp(x)+exp(4)^2))+
(4*exp(x)*x^3+9*x^5+16)*log(x)-4*exp(x)*x^4-9*x^6-4*x^3+4*x^2-16*x)/(9*x^5*log(x)-9*x^6),x, algorithm="fricas"
)

[Out]

-1/9*(x^4*log((x - log(x))*e^(e^8 + e^x))^2 - 9*x^5 - 4*x^2*log((x - log(x))*e^(e^8 + e^x)) + 4)/x^4

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giac [B]  time = 0.16, size = 96, normalized size = 2.91 \begin {gather*} -\frac {2 \, x^{4} e^{x} \log \left (x - \log \relax (x)\right ) + x^{4} \log \left (x - \log \relax (x)\right )^{2} + 2 \, x^{4} e^{8} \log \left (-x + \log \relax (x)\right ) - 9 \, x^{5} + x^{4} e^{\left (2 \, x\right )} + 2 \, x^{4} e^{\left (x + 8\right )} - 4 \, x^{2} e^{8} - 4 \, x^{2} e^{x} - 4 \, x^{2} \log \left (x - \log \relax (x)\right ) + 4}{9 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^5*exp(x)-8*x^2)*log(x)+2*x^6*exp(x)+2*x^5-2*x^4+8*x^3)*log((x-log(x))*exp(exp(x)+exp(4)^2))+
(4*exp(x)*x^3+9*x^5+16)*log(x)-4*exp(x)*x^4-9*x^6-4*x^3+4*x^2-16*x)/(9*x^5*log(x)-9*x^6),x, algorithm="giac")

[Out]

-1/9*(2*x^4*e^x*log(x - log(x)) + x^4*log(x - log(x))^2 + 2*x^4*e^8*log(-x + log(x)) - 9*x^5 + x^4*e^(2*x) + 2
*x^4*e^(x + 8) - 4*x^2*e^8 - 4*x^2*e^x - 4*x^2*log(x - log(x)) + 4)/x^4

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maple [C]  time = 0.33, size = 529, normalized size = 16.03

method	result	size
risch	\(-\frac {2 \left (\ln \left (x -\ln \relax (x )\right ) x^{2}+{\mathrm e}^{x} x^{2}-2\right ) \ln \left ({\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )}{9 x^{2}}+\frac {2 i \pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2}-i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2} {\mathrm e}^{x} x^{4}+i \pi \ln \left (\ln \relax (x )-x \right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) x^{4}+i \pi \ln \left (\ln \relax (x )-x \right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2} x^{4}-i \pi \ln \left (\ln \relax (x )-x \right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{3} x^{4}-2 i \pi \,x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )+2 i \pi \,x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{3}-i \pi \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{3} {\mathrm e}^{x} x^{4}-2 i \pi \,x^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2} {\mathrm e}^{x} x^{4}+i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )-x \right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) {\mathrm e}^{x} x^{4}-i \pi \ln \left (\ln \relax (x )-x \right ) \mathrm {csgn}\left (i {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-x \right ) {\mathrm e}^{{\mathrm e}^{x}+{\mathrm e}^{8}}\right )^{2} x^{4}+{\mathrm e}^{2 x} x^{4}-\ln \left (x -\ln \relax (x )\right )^{2} x^{4}+9 x^{5}+4 \ln \left (x -\ln \relax (x )\right ) x^{2}-4}{9 x^{4}}\)	\(529\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^5*exp(x)-8*x^2)*ln(x)+2*x^6*exp(x)+2*x^5-2*x^4+8*x^3)*ln((x-ln(x))*exp(exp(x)+exp(4)^2))+(4*exp(x)
*x^3+9*x^5+16)*ln(x)-4*exp(x)*x^4-9*x^6-4*x^3+4*x^2-16*x)/(9*x^5*ln(x)-9*x^6),x,method=_RETURNVERBOSE)

[Out]

-2/9*(ln(x-ln(x))*x^2+exp(x)*x^2-2)/x^2*ln(exp(exp(x)+exp(8)))+1/9*(2*I*Pi*x^2*csgn(I*exp(exp(x)+exp(8)))*csgn
(I*(ln(x)-x)*exp(exp(x)+exp(8)))^2-I*Pi*csgn(I*exp(exp(x)+exp(8)))*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^2*exp(
x)*x^4+I*Pi*ln(ln(x)-x)*csgn(I*(ln(x)-x))*csgn(I*exp(exp(x)+exp(8)))*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))*x^4+
I*Pi*ln(ln(x)-x)*csgn(I*(ln(x)-x))*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^2*x^4-I*Pi*ln(ln(x)-x)*csgn(I*(ln(x)-x
)*exp(exp(x)+exp(8)))^3*x^4-2*I*Pi*x^2*csgn(I*(ln(x)-x))*csgn(I*exp(exp(x)+exp(8)))*csgn(I*(ln(x)-x)*exp(exp(x
)+exp(8)))+2*I*Pi*x^2*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^3-I*Pi*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^3*exp(x
)*x^4-2*I*Pi*x^2*csgn(I*(ln(x)-x))*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^2+I*Pi*csgn(I*(ln(x)-x))*csgn(I*(ln(x)
-x)*exp(exp(x)+exp(8)))^2*exp(x)*x^4+I*Pi*csgn(I*(ln(x)-x))*csgn(I*exp(exp(x)+exp(8)))*csgn(I*(ln(x)-x)*exp(ex
p(x)+exp(8)))*exp(x)*x^4-I*Pi*ln(ln(x)-x)*csgn(I*exp(exp(x)+exp(8)))*csgn(I*(ln(x)-x)*exp(exp(x)+exp(8)))^2*x^
4+exp(2*x)*x^4-ln(x-ln(x))^2*x^4+9*x^5+4*ln(x-ln(x))*x^2-4)/x^4

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maxima [B]  time = 0.39, size = 83, normalized size = 2.52 \begin {gather*} -\frac {x^{4} \log \left (x - \log \relax (x)\right )^{2} - 9 \, x^{5} + x^{4} e^{\left (2 \, x\right )} - 4 \, x^{2} e^{8} + 2 \, {\left (x^{4} e^{8} - 2 \, x^{2}\right )} e^{x} + 2 \, {\left (x^{4} e^{8} + x^{4} e^{x} - 2 \, x^{2}\right )} \log \left (x - \log \relax (x)\right ) + 4}{9 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^5*exp(x)-8*x^2)*log(x)+2*x^6*exp(x)+2*x^5-2*x^4+8*x^3)*log((x-log(x))*exp(exp(x)+exp(4)^2))+
(4*exp(x)*x^3+9*x^5+16)*log(x)-4*exp(x)*x^4-9*x^6-4*x^3+4*x^2-16*x)/(9*x^5*log(x)-9*x^6),x, algorithm="maxima"
)

[Out]

-1/9*(x^4*log(x - log(x))^2 - 9*x^5 + x^4*e^(2*x) - 4*x^2*e^8 + 2*(x^4*e^8 - 2*x^2)*e^x + 2*(x^4*e^8 + x^4*e^x
- 2*x^2)*log(x - log(x)) + 4)/x^4

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mupad [B]  time = 3.73, size = 44, normalized size = 1.33 \begin {gather*} x+\frac {4\,\ln \left ({\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{{\mathrm {e}}^8}\,\left (x-\ln \relax (x)\right )\right )}{9\,x^2}-\frac {{\ln \left ({\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{{\mathrm {e}}^8}\,\left (x-\ln \relax (x)\right )\right )}^2}{9}-\frac {4}{9\,x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(16*x + 4*x^4*exp(x) - log(exp(exp(8) + exp(x))*(x - log(x)))*(2*x^6*exp(x) + 8*x^3 - 2*x^4 + 2*x^5 - log
(x)*(2*x^5*exp(x) + 8*x^2)) - 4*x^2 + 4*x^3 + 9*x^6 - log(x)*(4*x^3*exp(x) + 9*x^5 + 16))/(9*x^5*log(x) - 9*x^
6),x)

[Out]

x + (4*log(exp(exp(x))*exp(exp(8))*(x - log(x))))/(9*x^2) - log(exp(exp(x))*exp(exp(8))*(x - log(x)))^2/9 - 4/
(9*x^4)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**5*exp(x)-8*x**2)*ln(x)+2*x**6*exp(x)+2*x**5-2*x**4+8*x**3)*ln((x-ln(x))*exp(exp(x)+exp(4)**
2))+(4*exp(x)*x**3+9*x**5+16)*ln(x)-4*exp(x)*x**4-9*x**6-4*x**3+4*x**2-16*x)/(9*x**5*ln(x)-9*x**6),x)

[Out]

Timed out

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