3.75.31 \(\int \frac {e^{e^{\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}}+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}} (e^{2 x^2} (185-400 x^2)+e^{2 x^2} (42-60 x^2) \log (x)+e^{2 x^2} (-9+24 x^2) \log ^2(x)+e^{2 x^2} (-2+4 x^2) \log ^3(x))}{625 x^3} \, dx\)

Optimal. Leaf size=28 \[ e^{e^{\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}}} \]

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Rubi [F]  time = 102.11, 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 (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{625 x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2)) + (-1
00*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2))*(E^(2*x^2)*(185 - 4
00*x^2) + E^(2*x^2)*(42 - 60*x^2)*Log[x] + E^(2*x^2)*(-9 + 24*x^2)*Log[x]^2 + E^(2*x^2)*(-2 + 4*x^2)*Log[x]^3)
)/(625*x^3),x]

[Out]

(37*Defer[Int][E^(2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2))
+ (E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])^2)/(625*x^2))/x^3, x])/125 - (16*Defer[Int][E^(2*x^2 + E^((E^(2*x^2)*
(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)) + (E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])
^2)/(625*x^2))/x, x])/25 + (42*Defer[Int][(E^(2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))
/x^((3*E^(2*x^2))/(125*x^2)) + (E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])^2)/(625*x^2))*Log[x])/x^3, x])/625 - (12*
Defer[Int][(E^(2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)) +
(E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])^2)/(625*x^2))*Log[x])/x, x])/125 - (9*Defer[Int][(E^(2*x^2 + E^((E^(2*x^
2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)) + (E^(2*x^2)*(-4 + Log[x])*(5 + Log[
x])^2)/(625*x^2))*Log[x]^2)/x^3, x])/625 + (24*Defer[Int][(E^(2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x
]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)) + (E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])^2)/(625*x^2))*Log[x]^2)/x
, x])/625 - (2*Defer[Int][(E^(2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2)
)/(125*x^2)) + (E^(2*x^2)*(-4 + Log[x])*(5 + Log[x])^2)/(625*x^2))*Log[x]^3)/x^3, x])/625 + (4*Defer[Int][(E^(
2*x^2 + E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)) + (E^(2*x^2)*(-4
+ Log[x])*(5 + Log[x])^2)/(625*x^2))*Log[x]^3)/x, x])/625

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{625} \int \frac {\exp \left (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) \left (e^{2 x^2} \left (185-400 x^2\right )+e^{2 x^2} \left (42-60 x^2\right ) \log (x)+e^{2 x^2} \left (-9+24 x^2\right ) \log ^2(x)+e^{2 x^2} \left (-2+4 x^2\right ) \log ^3(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \frac {\exp \left (\exp \left (\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right )+2 x^2+\frac {-100 e^{2 x^2}-15 e^{2 x^2} \log (x)+6 e^{2 x^2} \log ^2(x)+e^{2 x^2} \log ^3(x)}{625 x^2}\right ) (5+\log (x)) \left (37-80 x^2+\log (x)+4 x^2 \log (x)-2 \log ^2(x)+4 x^2 \log ^2(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) (5+\log (x)) \left (37-80 x^2+\left (1+4 x^2\right ) \log (x)+\left (-2+4 x^2\right ) \log ^2(x)\right )}{x^3} \, dx\\ &=\frac {1}{625} \int \left (-\frac {5 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-37+80 x^2\right )}{x^3}-\frac {6 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-7+10 x^2\right ) \log (x)}{x^3}+\frac {3 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-3+8 x^2\right ) \log ^2(x)}{x^3}+\frac {2 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-1+2 x^2\right ) \log ^3(x)}{x^3}\right ) \, dx\\ &=\frac {2}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-1+2 x^2\right ) \log ^3(x)}{x^3} \, dx+\frac {3}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-3+8 x^2\right ) \log ^2(x)}{x^3} \, dx-\frac {1}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-37+80 x^2\right )}{x^3} \, dx-\frac {6}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \left (-7+10 x^2\right ) \log (x)}{x^3} \, dx\\ &=\frac {2}{625} \int \left (-\frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x^3}+\frac {2 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x}\right ) \, dx+\frac {3}{625} \int \left (-\frac {3 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x^3}+\frac {8 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x}\right ) \, dx-\frac {1}{125} \int \left (-\frac {37 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x^3}+\frac {80 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x}\right ) \, dx-\frac {6}{625} \int \left (-\frac {7 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x^3}+\frac {10 \exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x}\right ) \, dx\\ &=-\left (\frac {2}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x^3} \, dx\right )+\frac {4}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^3(x)}{x} \, dx-\frac {9}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x^3} \, dx+\frac {24}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log ^2(x)}{x} \, dx+\frac {42}{625} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x^3} \, dx-\frac {12}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right ) \log (x)}{x} \, dx+\frac {37}{125} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x^3} \, dx-\frac {16}{25} \int \frac {\exp \left (2 x^2+\exp \left (\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}\right ) x^{-\frac {3 e^{2 x^2}}{125 x^2}}+\frac {e^{2 x^2} (-4+\log (x)) (5+\log (x))^2}{625 x^2}\right )}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.60, size = 47, normalized size = 1.68 \begin {gather*} e^{e^{\frac {e^{2 x^2} \left (-100+6 \log ^2(x)+\log ^3(x)\right )}{625 x^2}} x^{-\frac {3 e^{2 x^2}}{125 x^2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2))
+ (-100*E^(2*x^2) - 15*E^(2*x^2)*Log[x] + 6*E^(2*x^2)*Log[x]^2 + E^(2*x^2)*Log[x]^3)/(625*x^2))*(E^(2*x^2)*(1
85 - 400*x^2) + E^(2*x^2)*(42 - 60*x^2)*Log[x] + E^(2*x^2)*(-9 + 24*x^2)*Log[x]^2 + E^(2*x^2)*(-2 + 4*x^2)*Log
[x]^3))/(625*x^3),x]

[Out]

E^(E^((E^(2*x^2)*(-100 + 6*Log[x]^2 + Log[x]^3))/(625*x^2))/x^((3*E^(2*x^2))/(125*x^2)))

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fricas [B]  time = 1.06, size = 149, normalized size = 5.32 \begin {gather*} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 625 \, x^{2} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \relax (x) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} + 6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \relax (x) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}} - \frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \relax (x) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x)^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(
-400*x^2+185)*exp(x^2)^2)*exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^
2)^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2)^2)/x^2))
/x^3,x, algorithm="fricas")

[Out]

e^(1/625*(e^(2*x^2)*log(x)^3 + 625*x^2*e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(
x) - 100*e^(2*x^2))/x^2) + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2 - 1/625*(e^(2*x^2)*
log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*x^2))/x^2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, {\left (2 \, x^{2} - 1\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 3 \, {\left (8 \, x^{2} - 3\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 6 \, {\left (10 \, x^{2} - 7\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x) - 5 \, {\left (80 \, x^{2} - 37\right )} e^{\left (2 \, x^{2}\right )}\right )} e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \relax (x) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}} + e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3} + 6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} - 15 \, e^{\left (2 \, x^{2}\right )} \log \relax (x) - 100 \, e^{\left (2 \, x^{2}\right )}}{625 \, x^{2}}\right )}\right )}}{625 \, x^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x)^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(
-400*x^2+185)*exp(x^2)^2)*exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^
2)^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2)^2)/x^2))
/x^3,x, algorithm="giac")

[Out]

integrate(1/625*(2*(2*x^2 - 1)*e^(2*x^2)*log(x)^3 + 3*(8*x^2 - 3)*e^(2*x^2)*log(x)^2 - 6*(10*x^2 - 7)*e^(2*x^2
)*log(x) - 5*(80*x^2 - 37)*e^(2*x^2))*e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x
) - 100*e^(2*x^2))/x^2 + e^(1/625*(e^(2*x^2)*log(x)^3 + 6*e^(2*x^2)*log(x)^2 - 15*e^(2*x^2)*log(x) - 100*e^(2*
x^2))/x^2))/x^3, x)

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maple [A]  time = 0.04, size = 24, normalized size = 0.86

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{2 x^{2}} \left (\ln \relax (x )-4\right ) \left (5+\ln \relax (x )\right )^{2}}{625 x^{2}}}}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/625*((4*x^2-2)*exp(x^2)^2*ln(x)^3+(24*x^2-9)*exp(x^2)^2*ln(x)^2+(-60*x^2+42)*exp(x^2)^2*ln(x)+(-400*x^2+
185)*exp(x^2)^2)*exp(1/625*(exp(x^2)^2*ln(x)^3+6*exp(x^2)^2*ln(x)^2-15*exp(x^2)^2*ln(x)-100*exp(x^2)^2)/x^2)*e
xp(exp(1/625*(exp(x^2)^2*ln(x)^3+6*exp(x^2)^2*ln(x)^2-15*exp(x^2)^2*ln(x)-100*exp(x^2)^2)/x^2))/x^3,x,method=_
RETURNVERBOSE)

[Out]

exp(exp(1/625*exp(2*x^2)*(ln(x)-4)*(5+ln(x))^2/x^2))

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maxima [B]  time = 1.92, size = 57, normalized size = 2.04 \begin {gather*} e^{\left (e^{\left (\frac {e^{\left (2 \, x^{2}\right )} \log \relax (x)^{3}}{625 \, x^{2}} + \frac {6 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2}}{625 \, x^{2}} - \frac {3 \, e^{\left (2 \, x^{2}\right )} \log \relax (x)}{125 \, x^{2}} - \frac {4 \, e^{\left (2 \, x^{2}\right )}}{25 \, x^{2}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((4*x^2-2)*exp(x^2)^2*log(x)^3+(24*x^2-9)*exp(x^2)^2*log(x)^2+(-60*x^2+42)*exp(x^2)^2*log(x)+(
-400*x^2+185)*exp(x^2)^2)*exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^
2)^2)/x^2)*exp(exp(1/625*(exp(x^2)^2*log(x)^3+6*exp(x^2)^2*log(x)^2-15*exp(x^2)^2*log(x)-100*exp(x^2)^2)/x^2))
/x^3,x, algorithm="maxima")

[Out]

e^(e^(1/625*e^(2*x^2)*log(x)^3/x^2 + 6/625*e^(2*x^2)*log(x)^2/x^2 - 3/125*e^(2*x^2)*log(x)/x^2 - 4/25*e^(2*x^2
)/x^2))

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mupad [B]  time = 4.75, size = 60, normalized size = 2.14 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^{2\,x^2}\,\ln \relax (x)}{125\,x^2}}\,{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^{2\,x^2}}{25\,x^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x^2}\,{\ln \relax (x)}^3}{625\,x^2}}\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^{2\,x^2}\,{\ln \relax (x)}^2}{625\,x^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-((4*exp(2*x^2))/25 - (6*exp(2*x^2)*log(x)^2)/625 - (exp(2*x^2)*log(x)^3)/625 + (3*exp(2*x^2)*log(x)
)/125)/x^2)*exp(exp(-((4*exp(2*x^2))/25 - (6*exp(2*x^2)*log(x)^2)/625 - (exp(2*x^2)*log(x)^3)/625 + (3*exp(2*x
^2)*log(x))/125)/x^2))*(exp(2*x^2)*(400*x^2 - 185) + exp(2*x^2)*log(x)*(60*x^2 - 42) - exp(2*x^2)*log(x)^3*(4*
x^2 - 2) - exp(2*x^2)*log(x)^2*(24*x^2 - 9)))/(625*x^3),x)

[Out]

exp(exp(-(3*exp(2*x^2)*log(x))/(125*x^2))*exp(-(4*exp(2*x^2))/(25*x^2))*exp((exp(2*x^2)*log(x)^3)/(625*x^2))*e
xp((6*exp(2*x^2)*log(x)^2)/(625*x^2)))

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sympy [B]  time = 11.33, size = 58, normalized size = 2.07 \begin {gather*} e^{e^{\frac {\frac {e^{2 x^{2}} \log {\relax (x )}^{3}}{625} + \frac {6 e^{2 x^{2}} \log {\relax (x )}^{2}}{625} - \frac {3 e^{2 x^{2}} \log {\relax (x )}}{125} - \frac {4 e^{2 x^{2}}}{25}}{x^{2}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/625*((4*x**2-2)*exp(x**2)**2*ln(x)**3+(24*x**2-9)*exp(x**2)**2*ln(x)**2+(-60*x**2+42)*exp(x**2)**2
*ln(x)+(-400*x**2+185)*exp(x**2)**2)*exp(1/625*(exp(x**2)**2*ln(x)**3+6*exp(x**2)**2*ln(x)**2-15*exp(x**2)**2*
ln(x)-100*exp(x**2)**2)/x**2)*exp(exp(1/625*(exp(x**2)**2*ln(x)**3+6*exp(x**2)**2*ln(x)**2-15*exp(x**2)**2*ln(
x)-100*exp(x**2)**2)/x**2))/x**3,x)

[Out]

exp(exp((exp(2*x**2)*log(x)**3/625 + 6*exp(2*x**2)*log(x)**2/625 - 3*exp(2*x**2)*log(x)/125 - 4*exp(2*x**2)/25
)/x**2))

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