3.59.69 \(\int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} (-8 x^5+(24 x^4+12 x^5) \log (x)+(-24 x^3-40 x^4) \log ^2(x)+(8 x^2+48 x^3) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x))}{\log ^5(x)} \, dx\)

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

________________________________________________________________________________________

Rubi [F]  time = 23.78, 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 {3 \log ^5(x)+2 \log ^6(x)+\exp \left (\exp \left (\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}\right )+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}\right ) \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3*Log[x]^5 + 2*Log[x]^6 + E^(E^((2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4
)/Log[x]^4) + (2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4)*(-8*x^5 + (
24*x^4 + 12*x^5)*Log[x] + (-24*x^3 - 40*x^4)*Log[x]^2 + (8*x^2 + 48*x^3)*Log[x]^3 - 24*x^2*Log[x]^4 + 4*x*Log[
x]^5))/Log[x]^5,x]

[Out]

x + 2*x*Log[x] + 4*Defer[Int][E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[
x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x, x] - 8*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^
2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^5)/Log[x]^5, x] + 24*Defer[Int
][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 -
(8*x^3)/Log[x])*x^4)/Log[x]^4, x] + 12*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Lo
g[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^5)/Log[x]^4, x] - 24*Defer[Int][(E^(E^((2*x^
2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x]
)*x^3)/Log[x]^3, x] - 40*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^
5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^4)/Log[x]^3, x] + 8*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^
4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^2)/Log[x]^2
, x] + 48*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + 2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (
12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^3)/Log[x]^2, x] - 24*Defer[Int][(E^(E^((2*x^2*(x - Log[x])^4)/Log[x]^4) +
2*x^2 + (2*x^6)/Log[x]^4 - (8*x^5)/Log[x]^3 + (12*x^4)/Log[x]^2 - (8*x^3)/Log[x])*x^2)/Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3+2 \log (x)+\frac {4 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x (x-\log (x))^3 \left (-2 x+3 x \log (x)-\log ^2(x)\right )}{\log ^5(x)}\right ) \, dx\\ &=3 x+2 \int \log (x) \, dx+4 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x (x-\log (x))^3 \left (-2 x+3 x \log (x)-\log ^2(x)\right )}{\log ^5(x)} \, dx\\ &=x+2 x \log (x)+4 \int \left (\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x-\frac {2 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^5(x)}+\frac {3 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4 (2+x)}{\log ^4(x)}-\frac {2 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3 (3+5 x)}{\log ^3(x)}+\frac {2 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2 (1+6 x)}{\log ^2(x)}-\frac {6 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log (x)}\right ) \, dx\\ &=x+2 x \log (x)+4 \int \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x \, dx-8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^5(x)} \, dx-8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3 (3+5 x)}{\log ^3(x)} \, dx+8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2 (1+6 x)}{\log ^2(x)} \, dx+12 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4 (2+x)}{\log ^4(x)} \, dx-24 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log (x)} \, dx\\ &=x+2 x \log (x)+4 \int \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x \, dx-8 \int \left (\frac {3 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3}{\log ^3(x)}+\frac {5 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4}{\log ^3(x)}\right ) \, dx+8 \int \left (\frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log ^2(x)}+\frac {6 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3}{\log ^2(x)}\right ) \, dx-8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^5(x)} \, dx+12 \int \left (\frac {2 \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4}{\log ^4(x)}+\frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^4(x)}\right ) \, dx-24 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log (x)} \, dx\\ &=x+2 x \log (x)+4 \int \exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x \, dx-8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^5(x)} \, dx+8 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log ^2(x)} \, dx+12 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^5}{\log ^4(x)} \, dx+24 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4}{\log ^4(x)} \, dx-24 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3}{\log ^3(x)} \, dx-24 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^2}{\log (x)} \, dx-40 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^4}{\log ^3(x)} \, dx+48 \int \frac {\exp \left (e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}+2 x^2+\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}\right ) x^3}{\log ^2(x)} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.35, size = 28, normalized size = 1.00 \begin {gather*} e^{e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}}+x+2 x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*Log[x]^5 + 2*Log[x]^6 + E^(E^((2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Lo
g[x]^4)/Log[x]^4) + (2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4)*(-8*x
^5 + (24*x^4 + 12*x^5)*Log[x] + (-24*x^3 - 40*x^4)*Log[x]^2 + (8*x^2 + 48*x^3)*Log[x]^3 - 24*x^2*Log[x]^4 + 4*
x*Log[x]^5))/Log[x]^5,x]

[Out]

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

________________________________________________________________________________________

fricas [B]  time = 0.67, size = 193, normalized size = 6.89 \begin {gather*} {\left ({\left (2 \, x \log \relax (x) + x\right )} e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \relax (x) + 6 \, x^{4} \log \relax (x)^{2} - 4 \, x^{3} \log \relax (x)^{3} + x^{2} \log \relax (x)^{4}\right )}}{\log \relax (x)^{4}}\right )} + e^{\left (\frac {2 \, x^{6} - 8 \, x^{5} \log \relax (x) + 12 \, x^{4} \log \relax (x)^{2} - 8 \, x^{3} \log \relax (x)^{3} + 2 \, x^{2} \log \relax (x)^{4} + e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \relax (x) + 6 \, x^{4} \log \relax (x)^{2} - 4 \, x^{3} \log \relax (x)^{3} + x^{2} \log \relax (x)^{4}\right )}}{\log \relax (x)^{4}}\right )} \log \relax (x)^{4}}{\log \relax (x)^{4}}\right )}\right )} e^{\left (-\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \relax (x) + 6 \, x^{4} \log \relax (x)^{2} - 4 \, x^{3} \log \relax (x)^{3} + x^{2} \log \relax (x)^{4}\right )}}{\log \relax (x)^{4}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4-24*x^3)*log(x)^2+(12*x^5+24*x^4)*log
(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log
(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x)^6+3*log(x)^5)/log(x)^5,x, algorit
hm="fricas")

[Out]

((2*x*log(x) + x)*e^(2*(x^6 - 4*x^5*log(x) + 6*x^4*log(x)^2 - 4*x^3*log(x)^3 + x^2*log(x)^4)/log(x)^4) + e^((2
*x^6 - 8*x^5*log(x) + 12*x^4*log(x)^2 - 8*x^3*log(x)^3 + 2*x^2*log(x)^4 + e^(2*(x^6 - 4*x^5*log(x) + 6*x^4*log
(x)^2 - 4*x^3*log(x)^3 + x^2*log(x)^4)/log(x)^4)*log(x)^4)/log(x)^4))*e^(-2*(x^6 - 4*x^5*log(x) + 6*x^4*log(x)
^2 - 4*x^3*log(x)^3 + x^2*log(x)^4)/log(x)^4)

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4-24*x^3)*log(x)^2+(12*x^5+24*x^4)*log
(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log
(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x)^6+3*log(x)^5)/log(x)^5,x, algorit
hm="giac")

[Out]

undef

________________________________________________________________________________________

maple [A]  time = 0.14, size = 27, normalized size = 0.96

method	result	size
risch	\(2 x \ln \relax (x )+x +{\mathrm e}^{{\mathrm e}^{\frac {2 x^{2} \left (\ln \relax (x )-x \right )^{4}}{\ln \relax (x )^{4}}}}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x*ln(x)^5-24*x^2*ln(x)^4+(48*x^3+8*x^2)*ln(x)^3+(-40*x^4-24*x^3)*ln(x)^2+(12*x^5+24*x^4)*ln(x)-8*x^5)*
exp((2*x^2*ln(x)^4-8*x^3*ln(x)^3+12*x^4*ln(x)^2-8*x^5*ln(x)+2*x^6)/ln(x)^4)*exp(exp((2*x^2*ln(x)^4-8*x^3*ln(x)
^3+12*x^4*ln(x)^2-8*x^5*ln(x)+2*x^6)/ln(x)^4))+2*ln(x)^6+3*ln(x)^5)/ln(x)^5,x,method=_RETURNVERBOSE)

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 1.10, size = 51, normalized size = 1.82 \begin {gather*} 2 \, x \log \relax (x) + x + e^{\left (e^{\left (2 \, x^{2} + \frac {2 \, x^{6}}{\log \relax (x)^{4}} - \frac {8 \, x^{5}}{\log \relax (x)^{3}} + \frac {12 \, x^{4}}{\log \relax (x)^{2}} - \frac {8 \, x^{3}}{\log \relax (x)}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4-24*x^3)*log(x)^2+(12*x^5+24*x^4)*log
(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log
(x)^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x)^6+3*log(x)^5)/log(x)^5,x, algorit
hm="maxima")

[Out]

2*x*log(x) + x + e^(e^(2*x^2 + 2*x^6/log(x)^4 - 8*x^5/log(x)^3 + 12*x^4/log(x)^2 - 8*x^3/log(x)))

________________________________________________________________________________________

mupad [B]  time = 4.30, size = 55, normalized size = 1.96 \begin {gather*} x+{\mathrm {e}}^{{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^{-\frac {8\,x^3}{\ln \relax (x)}}\,{\mathrm {e}}^{\frac {2\,x^6}{{\ln \relax (x)}^4}}\,{\mathrm {e}}^{-\frac {8\,x^5}{{\ln \relax (x)}^3}}\,{\mathrm {e}}^{\frac {12\,x^4}{{\ln \relax (x)}^2}}}+2\,x\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*log(x)^5 + 2*log(x)^6 + exp((2*x^2*log(x)^4 - 8*x^5*log(x) - 8*x^3*log(x)^3 + 12*x^4*log(x)^2 + 2*x^6)/
log(x)^4)*exp(exp((2*x^2*log(x)^4 - 8*x^5*log(x) - 8*x^3*log(x)^3 + 12*x^4*log(x)^2 + 2*x^6)/log(x)^4))*(log(x
)*(24*x^4 + 12*x^5) + 4*x*log(x)^5 + log(x)^3*(8*x^2 + 48*x^3) - log(x)^2*(24*x^3 + 40*x^4) - 24*x^2*log(x)^4
- 8*x^5))/log(x)^5,x)

[Out]

x + exp(exp(2*x^2)*exp(-(8*x^3)/log(x))*exp((2*x^6)/log(x)^4)*exp(-(8*x^5)/log(x)^3)*exp((12*x^4)/log(x)^2)) +
2*x*log(x)

________________________________________________________________________________________

sympy [B]  time = 2.23, size = 60, normalized size = 2.14 \begin {gather*} 2 x \log {\relax (x )} + x + e^{e^{\frac {2 x^{6} - 8 x^{5} \log {\relax (x )} + 12 x^{4} \log {\relax (x )}^{2} - 8 x^{3} \log {\relax (x )}^{3} + 2 x^{2} \log {\relax (x )}^{4}}{\log {\relax (x )}^{4}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x*ln(x)**5-24*x**2*ln(x)**4+(48*x**3+8*x**2)*ln(x)**3+(-40*x**4-24*x**3)*ln(x)**2+(12*x**5+24*x*
*4)*ln(x)-8*x**5)*exp((2*x**2*ln(x)**4-8*x**3*ln(x)**3+12*x**4*ln(x)**2-8*x**5*ln(x)+2*x**6)/ln(x)**4)*exp(exp
((2*x**2*ln(x)**4-8*x**3*ln(x)**3+12*x**4*ln(x)**2-8*x**5*ln(x)+2*x**6)/ln(x)**4))+2*ln(x)**6+3*ln(x)**5)/ln(x
)**5,x)

[Out]

2*x*log(x) + x + exp(exp((2*x**6 - 8*x**5*log(x) + 12*x**4*log(x)**2 - 8*x**3*log(x)**3 + 2*x**2*log(x)**4)/lo
g(x)**4))

________________________________________________________________________________________