3.25.5 \(\int \frac {e^{\frac {x^2+x \log (x)}{-x+\log (\frac {e^6 (9 x^2-6 x^3+x^4)+e^3 (-6 x+2 x^2) \log (x)+\log ^2(x)}{e^6 x^2})}} (-2 x+e^3 (3 x^2-x^4)+(-2+x-x^2-2 e^3 x^2) \log (x)+2 \log ^2(x)+(e^3 (-3 x-5 x^2+2 x^3)+(1+2 x+e^3 (-3 x+x^2)) \log (x)+\log ^2(x)) \log (\frac {e^6 (9 x^2-6 x^3+x^4)+e^3 (-6 x+2 x^2) \log (x)+\log ^2(x)}{e^6 x^2}))}{e^3 (-3 x^3+x^4)+x^2 \log (x)+(e^3 (6 x^2-2 x^3)-2 x \log (x)) \log (\frac {e^6 (9 x^2-6 x^3+x^4)+e^3 (-6 x+2 x^2) \log (x)+\log ^2(x)}{e^6 x^2})+(e^3 (-3 x+x^2)+\log (x)) \log ^2(\frac {e^6 (9 x^2-6 x^3+x^4)+e^3 (-6 x+2 x^2) \log (x)+\log ^2(x)}{e^6 x^2})} \, dx\)

Optimal. Leaf size=29 \[ e^{\frac {x (x+\log (x))}{-x+\log \left (\left (-3+x+\frac {\log (x)}{e^3 x}\right )^2\right )}} \]

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Rubi [F]  time = 120.41, 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^2+x \log (x)}{-x+\log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )}\right ) \left (-2 x+e^3 \left (3 x^2-x^4\right )+\left (-2+x-x^2-2 e^3 x^2\right ) \log (x)+2 \log ^2(x)+\left (e^3 \left (-3 x-5 x^2+2 x^3\right )+\left (1+2 x+e^3 \left (-3 x+x^2\right )\right ) \log (x)+\log ^2(x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )\right )}{e^3 \left (-3 x^3+x^4\right )+x^2 \log (x)+\left (e^3 \left (6 x^2-2 x^3\right )-2 x \log (x)\right ) \log \left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )+\left (e^3 \left (-3 x+x^2\right )+\log (x)\right ) \log ^2\left (\frac {e^6 \left (9 x^2-6 x^3+x^4\right )+e^3 \left (-6 x+2 x^2\right ) \log (x)+\log ^2(x)}{e^6 x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((x^2 + x*Log[x])/(-x + Log[(E^6*(9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E^6*x^2
)]))*(-2*x + E^3*(3*x^2 - x^4) + (-2 + x - x^2 - 2*E^3*x^2)*Log[x] + 2*Log[x]^2 + (E^3*(-3*x - 5*x^2 + 2*x^3)
+ (1 + 2*x + E^3*(-3*x + x^2))*Log[x] + Log[x]^2)*Log[(E^6*(9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] +
Log[x]^2)/(E^6*x^2)]))/(E^3*(-3*x^3 + x^4) + x^2*Log[x] + (E^3*(6*x^2 - 2*x^3) - 2*x*Log[x])*Log[(E^6*(9*x^2
- 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E^6*x^2)] + (E^3*(-3*x + x^2) + Log[x])*Log[(E^6*(9*x^
2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E^6*x^2)]^2),x]

[Out]

-2*Defer[Int][x^(1 - x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))/(E^(x^2/(x - Log[(E^3*(-3 + x)*x + Lo
g[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])^2), x] - 5*Def
er[Int][(E^(3 - x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(3 - x/(x - Log[(E^3*(-3 + x)*x + Log[
x])^2/(E^6*x^2)])))/((E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])^2), x] + Defer
[Int][(E^(3 - x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(4 - x/(x - Log[(E^3*(-3 + x)*x + Log[x]
)^2/(E^6*x^2)])))/((E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])^2), x] + 2*Defer
[Int][(x^(1 - x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*Log[x])/(E^(x^2/(x - Log[(E^3*(-3 + x)*x + L
og[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])^2), x] + (1 -
5*E^3)*Defer[Int][(x^(2 - x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*Log[x])/(E^(x^2/(x - Log[(E^3*(
-3 + x)*x + Log[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])^
2), x] + Defer[Int][(E^(3 - x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(3 - x/(x - Log[(E^3*(-3 +
x)*x + Log[x])^2/(E^6*x^2)]))*Log[x])/((E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^
2)])^2), x] - 2*Defer[Int][Log[x]/(E^(x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(x/(x - Log[(E^3
*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]
)^2), x] + Defer[Int][(x^(1 - x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*Log[x]^2)/(E^(x^2/(x - Log[(
E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^
2)])^2), x] + 2*Defer[Int][Log[x]^2/(E^(x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(x/(x - Log[(E
^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*(E^3*(-3 + x)*x + Log[x])*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2
)])^2), x] - 2*Defer[Int][x^(1 - x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))/(E^(x^2/(x - Log[(E^3*(-3
+ x)*x + Log[x])^2/(E^6*x^2)]))*(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])), x] - Defer[Int][Log[x]/(E^
(x^2/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*
(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)])), x] + Defer[Int][1/(E^(x^2/(x - Log[(E^3*(-3 + x)*x + Log[x]
)^2/(E^6*x^2)]))*x^(x/(x - Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*(-x + Log[(E^3*(-3 + x)*x + Log[x])^2/
(E^6*x^2)])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \left (\log ^2(x) \left (2+\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )-x \left (2+e^3 x \left (-3+x^2\right )+e^3 \left (3+5 x-2 x^2\right ) \log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )+\log (x) \left (-2+x-x^2-2 e^3 x^2+\left (1+\left (2-3 e^3\right ) x+e^3 x^2\right ) \log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )\right )}{\left (e^3 (-3+x) x+\log (x)\right ) \left (x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )^2} \, dx\\ &=\int \left (\frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \left (2 x+5 e^3 x^3-e^3 x^4+2 \log (x)-2 x \log (x)-\left (1-5 e^3\right ) x^2 \log (x)-e^3 x^3 \log (x)-2 \log ^2(x)-x \log ^2(x)\right )}{\left (3 e^3 x-e^3 x^2-\log (x)\right ) \left (x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )^2}+\frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} (-1-2 x-\log (x))}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) \, dx\\ &=\int \frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \left (2 x+5 e^3 x^3-e^3 x^4+2 \log (x)-2 x \log (x)-\left (1-5 e^3\right ) x^2 \log (x)-e^3 x^3 \log (x)-2 \log ^2(x)-x \log ^2(x)\right )}{\left (3 e^3 x-e^3 x^2-\log (x)\right ) \left (x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )^2} \, dx+\int \frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} (-1-2 x-\log (x))}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )} \, dx\\ &=\int \frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \left (x \left (-2+e^3 (-5+x) x^2\right )+\left (-2+2 x+\left (1-5 e^3\right ) x^2+e^3 x^3\right ) \log (x)+(2+x) \log ^2(x)\right )}{\left (e^3 (-3+x) x+\log (x)\right ) \left (x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )\right )^2} \, dx+\int \left (-\frac {2 \exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{1-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}}}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}-\frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \log (x)}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}+\frac {\exp \left (-\frac {x^2}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) x^{-\frac {x}{x-\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}}}{-x+\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.39, size = 65, normalized size = 2.24 \begin {gather*} e^{\frac {x^2}{-x+\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} x^{\frac {x}{-x+\log \left (\frac {\left (e^3 (-3+x) x+\log (x)\right )^2}{e^6 x^2}\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((x^2 + x*Log[x])/(-x + Log[(E^6*(9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E
^6*x^2)]))*(-2*x + E^3*(3*x^2 - x^4) + (-2 + x - x^2 - 2*E^3*x^2)*Log[x] + 2*Log[x]^2 + (E^3*(-3*x - 5*x^2 + 2
*x^3) + (1 + 2*x + E^3*(-3*x + x^2))*Log[x] + Log[x]^2)*Log[(E^6*(9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Lo
g[x] + Log[x]^2)/(E^6*x^2)]))/(E^3*(-3*x^3 + x^4) + x^2*Log[x] + (E^3*(6*x^2 - 2*x^3) - 2*x*Log[x])*Log[(E^6*(
9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E^6*x^2)] + (E^3*(-3*x + x^2) + Log[x])*Log[(E^6
*(9*x^2 - 6*x^3 + x^4) + E^3*(-6*x + 2*x^2)*Log[x] + Log[x]^2)/(E^6*x^2)]^2),x]

[Out]

E^(x^2/(-x + Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)]))*x^(x/(-x + Log[(E^3*(-3 + x)*x + Log[x])^2/(E^6*x^2)
]))

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fricas [B]  time = 0.98, size = 59, normalized size = 2.03 \begin {gather*} e^{\left (-\frac {x^{2} + x \log \relax (x)}{x - \log \left (\frac {{\left (2 \, {\left (x^{2} - 3 \, x\right )} e^{3} \log \relax (x) + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{6} + \log \relax (x)^{2}\right )} e^{\left (-6\right )}}{x^{2}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)^2+((x^2-3*x)*exp(3)+2*x+1)*log(x)+(2*x^3-5*x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3
)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)+2*log(x)^2+(-2*x^2*exp(3)-x^2+x-2)*log(x)+(-x^4+3*x^2)*exp(
3)-2*x)*exp((x*log(x)+x^2)/(log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)-
x))/((log(x)+(x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^
2)^2+(-2*x*log(x)+(-2*x^3+6*x^2)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x
^2/exp(3)^2)+x^2*log(x)+(x^4-3*x^3)*exp(3)),x, algorithm="fricas")

[Out]

e^(-(x^2 + x*log(x))/(x - log((2*(x^2 - 3*x)*e^3*log(x) + (x^4 - 6*x^3 + 9*x^2)*e^6 + log(x)^2)*e^(-6)/x^2)))

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giac [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(((log(x)^2+((x^2-3*x)*exp(3)+2*x+1)*log(x)+(2*x^3-5*x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3
)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)+2*log(x)^2+(-2*x^2*exp(3)-x^2+x-2)*log(x)+(-x^4+3*x^2)*exp(
3)-2*x)*exp((x*log(x)+x^2)/(log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)-
x))/((log(x)+(x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^
2)^2+(-2*x*log(x)+(-2*x^3+6*x^2)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x
^2/exp(3)^2)+x^2*log(x)+(x^4-3*x^3)*exp(3)),x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 456.63, size = 356, normalized size = 12.28

method	result	size
risch	\({\mathrm e}^{-\frac {2 x \left (x +\ln \relax (x )\right )}{i \pi \mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}\right )^{3}-2 i \pi \mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )\right )+i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )\right )^{2}-i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}}{x^{2}}\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right )-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+i \pi \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}}{x^{2}}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )^{2}}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )+4 \ln \relax (x )-4 \ln \left (\ln \relax (x )+\left (x^{2}-3 x \right ) {\mathrm e}^{3}\right )+2 x +12}}\)	\(356\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(x)^2+((x^2-3*x)*exp(3)+2*x+1)*ln(x)+(2*x^3-5*x^2-3*x)*exp(3))*ln((ln(x)^2+(2*x^2-6*x)*exp(3)*ln(x)+(x
^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)+2*ln(x)^2+(-2*x^2*exp(3)-x^2+x-2)*ln(x)+(-x^4+3*x^2)*exp(3)-2*x)*exp((
x*ln(x)+x^2)/(ln((ln(x)^2+(2*x^2-6*x)*exp(3)*ln(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)-x))/((ln(x)+(x^2-
3*x)*exp(3))*ln((ln(x)^2+(2*x^2-6*x)*exp(3)*ln(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)^2+(-2*x*ln(x)+(-2*
x^3+6*x^2)*exp(3))*ln((ln(x)^2+(2*x^2-6*x)*exp(3)*ln(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)+x^2*ln(x)+(x
^4-3*x^3)*exp(3)),x,method=_RETURNVERBOSE)

[Out]

exp(-2*x*(x+ln(x))/(I*Pi*csgn(I*(ln(x)+(x^2-3*x)*exp(3))^2)^3-2*I*Pi*csgn(I*(ln(x)+(x^2-3*x)*exp(3))^2)^2*csgn
(I*(ln(x)+(x^2-3*x)*exp(3)))+I*Pi*csgn(I*(ln(x)+(x^2-3*x)*exp(3))^2)*csgn(I*(ln(x)+(x^2-3*x)*exp(3)))^2-I*Pi*c
sgn(I*(ln(x)+(x^2-3*x)*exp(3))^2)*csgn(I/x^2*(ln(x)+(x^2-3*x)*exp(3))^2)^2+I*Pi*csgn(I*(ln(x)+(x^2-3*x)*exp(3)
)^2)*csgn(I/x^2*(ln(x)+(x^2-3*x)*exp(3))^2)*csgn(I/x^2)-I*Pi*csgn(I*x^2)^3+2*I*Pi*csgn(I*x^2)^2*csgn(I*x)-I*Pi
*csgn(I*x^2)*csgn(I*x)^2+I*Pi*csgn(I/x^2*(ln(x)+(x^2-3*x)*exp(3))^2)^3-I*Pi*csgn(I/x^2*(ln(x)+(x^2-3*x)*exp(3)
)^2)^2*csgn(I/x^2)+4*ln(x)-4*ln(ln(x)+(x^2-3*x)*exp(3))+2*x+12))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {{\left ({\left (x^{4} - 3 \, x^{2}\right )} e^{3} + {\left (2 \, x^{2} e^{3} + x^{2} - x + 2\right )} \log \relax (x) - 2 \, \log \relax (x)^{2} - {\left ({\left (2 \, x^{3} - 5 \, x^{2} - 3 \, x\right )} e^{3} + {\left ({\left (x^{2} - 3 \, x\right )} e^{3} + 2 \, x + 1\right )} \log \relax (x) + \log \relax (x)^{2}\right )} \log \left (\frac {{\left (2 \, {\left (x^{2} - 3 \, x\right )} e^{3} \log \relax (x) + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{6} + \log \relax (x)^{2}\right )} e^{\left (-6\right )}}{x^{2}}\right ) + 2 \, x\right )} e^{\left (-\frac {x^{2} + x \log \relax (x)}{x - \log \left (\frac {{\left (2 \, {\left (x^{2} - 3 \, x\right )} e^{3} \log \relax (x) + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{6} + \log \relax (x)^{2}\right )} e^{\left (-6\right )}}{x^{2}}\right )}\right )}}{x^{2} \log \relax (x) + {\left ({\left (x^{2} - 3 \, x\right )} e^{3} + \log \relax (x)\right )} \log \left (\frac {{\left (2 \, {\left (x^{2} - 3 \, x\right )} e^{3} \log \relax (x) + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{6} + \log \relax (x)^{2}\right )} e^{\left (-6\right )}}{x^{2}}\right )^{2} + {\left (x^{4} - 3 \, x^{3}\right )} e^{3} - 2 \, {\left ({\left (x^{3} - 3 \, x^{2}\right )} e^{3} + x \log \relax (x)\right )} \log \left (\frac {{\left (2 \, {\left (x^{2} - 3 \, x\right )} e^{3} \log \relax (x) + {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} e^{6} + \log \relax (x)^{2}\right )} e^{\left (-6\right )}}{x^{2}}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)^2+((x^2-3*x)*exp(3)+2*x+1)*log(x)+(2*x^3-5*x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3
)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)+2*log(x)^2+(-2*x^2*exp(3)-x^2+x-2)*log(x)+(-x^4+3*x^2)*exp(
3)-2*x)*exp((x*log(x)+x^2)/(log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^2)-
x))/((log(x)+(x^2-3*x)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x^2/exp(3)^
2)^2+(-2*x*log(x)+(-2*x^3+6*x^2)*exp(3))*log((log(x)^2+(2*x^2-6*x)*exp(3)*log(x)+(x^4-6*x^3+9*x^2)*exp(3)^2)/x
^2/exp(3)^2)+x^2*log(x)+(x^4-3*x^3)*exp(3)),x, algorithm="maxima")

[Out]

-integrate(((x^4 - 3*x^2)*e^3 + (2*x^2*e^3 + x^2 - x + 2)*log(x) - 2*log(x)^2 - ((2*x^3 - 5*x^2 - 3*x)*e^3 + (
(x^2 - 3*x)*e^3 + 2*x + 1)*log(x) + log(x)^2)*log((2*(x^2 - 3*x)*e^3*log(x) + (x^4 - 6*x^3 + 9*x^2)*e^6 + log(
x)^2)*e^(-6)/x^2) + 2*x)*e^(-(x^2 + x*log(x))/(x - log((2*(x^2 - 3*x)*e^3*log(x) + (x^4 - 6*x^3 + 9*x^2)*e^6 +
log(x)^2)*e^(-6)/x^2)))/(x^2*log(x) + ((x^2 - 3*x)*e^3 + log(x))*log((2*(x^2 - 3*x)*e^3*log(x) + (x^4 - 6*x^3
+ 9*x^2)*e^6 + log(x)^2)*e^(-6)/x^2)^2 + (x^4 - 3*x^3)*e^3 - 2*((x^3 - 3*x^2)*e^3 + x*log(x))*log((2*(x^2 - 3
*x)*e^3*log(x) + (x^4 - 6*x^3 + 9*x^2)*e^6 + log(x)^2)*e^(-6)/x^2)), x)

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mupad [B]  time = 3.81, size = 109, normalized size = 3.76 \begin {gather*} {\mathrm {e}}^{-\frac {x^2}{x-\ln \left (\frac {x^4-6\,x^3+2\,{\mathrm {e}}^{-3}\,x^2\,\ln \relax (x)+9\,x^2-6\,{\mathrm {e}}^{-3}\,x\,\ln \relax (x)+{\mathrm {e}}^{-6}\,{\ln \relax (x)}^2}{x^2}\right )}}\,{\mathrm {e}}^{-\frac {x\,\ln \relax (x)}{x-\ln \left (\frac {x^4-6\,x^3+2\,{\mathrm {e}}^{-3}\,x^2\,\ln \relax (x)+9\,x^2-6\,{\mathrm {e}}^{-3}\,x\,\ln \relax (x)+{\mathrm {e}}^{-6}\,{\ln \relax (x)}^2}{x^2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(x*log(x) + x^2)/(x - log((exp(-6)*(log(x)^2 + exp(6)*(9*x^2 - 6*x^3 + x^4) - exp(3)*log(x)*(6*x - 2
*x^2)))/x^2)))*(2*log(x)^2 - 2*x + log((exp(-6)*(log(x)^2 + exp(6)*(9*x^2 - 6*x^3 + x^4) - exp(3)*log(x)*(6*x
- 2*x^2)))/x^2)*(log(x)^2 - exp(3)*(3*x + 5*x^2 - 2*x^3) + log(x)*(2*x - exp(3)*(3*x - x^2) + 1)) + exp(3)*(3*
x^2 - x^4) - log(x)*(2*x^2*exp(3) - x + x^2 + 2)))/(x^2*log(x) + log((exp(-6)*(log(x)^2 + exp(6)*(9*x^2 - 6*x^
3 + x^4) - exp(3)*log(x)*(6*x - 2*x^2)))/x^2)*(exp(3)*(6*x^2 - 2*x^3) - 2*x*log(x)) + log((exp(-6)*(log(x)^2 +
exp(6)*(9*x^2 - 6*x^3 + x^4) - exp(3)*log(x)*(6*x - 2*x^2)))/x^2)^2*(log(x) - exp(3)*(3*x - x^2)) - exp(3)*(3
*x^3 - x^4)),x)

[Out]

exp(-x^2/(x - log((exp(-6)*log(x)^2 + 9*x^2 - 6*x^3 + x^4 - 6*x*exp(-3)*log(x) + 2*x^2*exp(-3)*log(x))/x^2)))*
exp(-(x*log(x))/(x - log((exp(-6)*log(x)^2 + 9*x^2 - 6*x^3 + x^4 - 6*x*exp(-3)*log(x) + 2*x^2*exp(-3)*log(x))/
x^2)))

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sympy [B]  time = 44.42, size = 56, normalized size = 1.93 \begin {gather*} e^{\frac {x^{2} + x \log {\relax (x )}}{- x + \log {\left (\frac {\left (2 x^{2} - 6 x\right ) e^{3} \log {\relax (x )} + \left (x^{4} - 6 x^{3} + 9 x^{2}\right ) e^{6} + \log {\relax (x )}^{2}}{x^{2} e^{6}} \right )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(x)**2+((x**2-3*x)*exp(3)+2*x+1)*ln(x)+(2*x**3-5*x**2-3*x)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp
(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(3)**2)/x**2/exp(3)**2)+2*ln(x)**2+(-2*x**2*exp(3)-x**2+x-2)*ln(x)+(-x**4+3*
x**2)*exp(3)-2*x)*exp((x*ln(x)+x**2)/(ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(3)**2)/x
**2/exp(3)**2)-x))/((ln(x)+(x**2-3*x)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*x**3+9*x**2)*exp(
3)**2)/x**2/exp(3)**2)**2+(-2*x*ln(x)+(-2*x**3+6*x**2)*exp(3))*ln((ln(x)**2+(2*x**2-6*x)*exp(3)*ln(x)+(x**4-6*
x**3+9*x**2)*exp(3)**2)/x**2/exp(3)**2)+x**2*ln(x)+(x**4-3*x**3)*exp(3)),x)

[Out]

exp((x**2 + x*log(x))/(-x + log(((2*x**2 - 6*x)*exp(3)*log(x) + (x**4 - 6*x**3 + 9*x**2)*exp(6) + log(x)**2)*e
xp(-6)/x**2)))

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