\(\int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+(12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x) \log (e^{-2 e^{\frac {1}{3} (12-7 x)}} (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)))}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx\) [855]

Optimal result

Integrand size = 135, antiderivative size = 27 \[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=x+\log ^2\left (20 \left (4 e^{-e^{4-\frac {7 x}{3}}}+\log (x)\right )^2\right ) \]

[Out]

x+ln(20*(ln(x)+4/exp(exp(-7/3*x+4)))^2)^2

Rubi [F]

\[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=\int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx \]

[In]

Int[(12*x + 3*E^E^((12 - 7*x)/3)*x*Log[x] + (12*E^E^((12 - 7*x)/3) + 112*E^((12 - 7*x)/3)*x)*Log[(320 + 160*E^
E^((12 - 7*x)/3)*Log[x] + 20*E^(2*E^((12 - 7*x)/3))*Log[x]^2)/E^(2*E^((12 - 7*x)/3))])/(12*x + 3*E^E^((12 - 7*
x)/3)*x*Log[x]),x]

[Out]

x + 4*Defer[Int][Log[(20*(4 + E^E^(4 - (7*x)/3)*Log[x])^2)/E^(2*E^(4 - (7*x)/3))]/(x*Log[x]), x] + (112*Defer[
Int][(E^(4 - (7*x)/3)*Log[(20*(4 + E^E^(4 - (7*x)/3)*Log[x])^2)/E^(2*E^(4 - (7*x)/3))])/(4 + E^E^(4 - (7*x)/3)
*Log[x]), x])/3 - 16*Defer[Int][Log[(20*(4 + E^E^(4 - (7*x)/3)*Log[x])^2)/E^(2*E^(4 - (7*x)/3))]/(x*Log[x]*(4
+ E^E^(4 - (7*x)/3)*Log[x])), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{3 x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \left (\frac {112 e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)}+\frac {3 \left (4 x+e^{e^{4-\frac {7 x}{3}}} x \log (x)+4 e^{e^{4-\frac {7 x}{3}}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )}\right ) \, dx \\ & = \frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \frac {4 x+e^{e^{4-\frac {7 x}{3}}} x \log (x)+4 e^{e^{4-\frac {7 x}{3}}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx \\ & = \frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \left (-\frac {16 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )}+\frac {x \log (x)+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)}\right ) \, dx \\ & = -\left (16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\right )+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \frac {x \log (x)+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)} \, dx \\ & = -\left (16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\right )+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \left (1+\frac {4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)}\right ) \, dx \\ & = x+4 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)} \, dx-16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(166\) vs. \(2(27)=54\).

Time = 0.32 (sec) , antiderivative size = 166, normalized size of antiderivative = 6.15 \[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=-4 e^{8-\frac {14 x}{3}}+x+\log ^2\left (\left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )-4 e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )+\log \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right ) \left (8 e^{4-\frac {7 x}{3}}-4 \log \left (\left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )\right ) \]

[In]

Integrate[(12*x + 3*E^E^((12 - 7*x)/3)*x*Log[x] + (12*E^E^((12 - 7*x)/3) + 112*E^((12 - 7*x)/3)*x)*Log[(320 +
160*E^E^((12 - 7*x)/3)*Log[x] + 20*E^(2*E^((12 - 7*x)/3))*Log[x]^2)/E^(2*E^((12 - 7*x)/3))])/(12*x + 3*E^E^((1
2 - 7*x)/3)*x*Log[x]),x]

[Out]

-4*E^(8 - (14*x)/3) + x + Log[(4 + E^E^(4 - (7*x)/3)*Log[x])^2]^2 - 4*E^(4 - (7*x)/3)*Log[(20*(4 + E^E^(4 - (7
*x)/3)*Log[x])^2)/E^(2*E^(4 - (7*x)/3))] + Log[4 + E^E^(4 - (7*x)/3)*Log[x]]*(8*E^(4 - (7*x)/3) - 4*Log[(4 + E
^E^(4 - (7*x)/3)*Log[x])^2] + 4*Log[(20*(4 + E^E^(4 - (7*x)/3)*Log[x])^2)/E^(2*E^(4 - (7*x)/3))])

Maple [F]

\[\int \frac {\left (12 \,{\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+112 x \,{\mathrm e}^{-\frac {7 x}{3}+4}\right ) \ln \left (\left (20 \ln \left (x \right )^{2} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {7 x}{3}+4}}+160 \ln \left (x \right ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+320\right ) {\mathrm e}^{-2 \,{\mathrm e}^{-\frac {7 x}{3}+4}}\right )+3 x \ln \left (x \right ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+12 x}{3 x \ln \left (x \right ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+12 x}d x\]

[In]

int(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*ln((20*ln(x)^2*exp(exp(-7/3*x+4))^2+160*ln(x)*exp(exp(-7/3*x+
4))+320)/exp(exp(-7/3*x+4))^2)+3*x*ln(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*ln(x)*exp(exp(-7/3*x+4))+12*x),x)

[Out]

int(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*ln((20*ln(x)^2*exp(exp(-7/3*x+4))^2+160*ln(x)*exp(exp(-7/3*x+
4))+320)/exp(exp(-7/3*x+4))^2)+3*x*ln(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*ln(x)*exp(exp(-7/3*x+4))+12*x),x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.59 \[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=\log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right )^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )^{2} + x \]

[In]

integrate(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*log((20*log(x)^2*exp(exp(-7/3*x+4))^2+160*log(x)*exp(ex
p(-7/3*x+4))+320)/exp(exp(-7/3*x+4))^2)+3*x*log(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*log(x)*exp(exp(-7/3*x+4))+12*
x),x, algorithm="fricas")

[Out]

log(20*(e^(2*e^(-7/3*x + 4))*log(x)^2 + 8*e^(e^(-7/3*x + 4))*log(x) + 16)*e^(-2*e^(-7/3*x + 4)))^2 + x

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).

Time = 1.22 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.89 \[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=x + \log {\left (\left (20 e^{2 e^{4 - \frac {7 x}{3}}} \log {\left (x \right )}^{2} + 160 e^{e^{4 - \frac {7 x}{3}}} \log {\left (x \right )} + 320\right ) e^{- 2 e^{4 - \frac {7 x}{3}}} \right )}^{2} \]

[In]

integrate(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*ln((20*ln(x)**2*exp(exp(-7/3*x+4))**2+160*ln(x)*exp(exp
(-7/3*x+4))+320)/exp(exp(-7/3*x+4))**2)+3*x*ln(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*ln(x)*exp(exp(-7/3*x+4))+12*x)
,x)

[Out]

x + log((20*exp(2*exp(4 - 7*x/3))*log(x)**2 + 160*exp(exp(4 - 7*x/3))*log(x) + 320)*exp(-2*exp(4 - 7*x/3)))**2

Maxima [F]

\[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=\int { \frac {3 \, x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 4 \, {\left (28 \, x e^{\left (-\frac {7}{3} \, x + 4\right )} + 3 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )} \log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right )^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right ) + 12 \, x}{3 \, {\left (x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 4 \, x\right )}} \,d x } \]

[In]

integrate(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*log((20*log(x)^2*exp(exp(-7/3*x+4))^2+160*log(x)*exp(ex
p(-7/3*x+4))+320)/exp(exp(-7/3*x+4))^2)+3*x*log(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*log(x)*exp(exp(-7/3*x+4))+12*
x),x, algorithm="maxima")

[Out]

1/3*integrate((3*x*e^(e^(-7/3*x + 4))*log(x) + 4*(28*x*e^(-7/3*x + 4) + 3*e^(e^(-7/3*x + 4)))*log(20*(e^(2*e^(
-7/3*x + 4))*log(x)^2 + 8*e^(e^(-7/3*x + 4))*log(x) + 16)*e^(-2*e^(-7/3*x + 4))) + 12*x)/(x*e^(e^(-7/3*x + 4))
*log(x) + 4*x), x)

Giac [F]

\[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx=\int { \frac {3 \, x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 4 \, {\left (28 \, x e^{\left (-\frac {7}{3} \, x + 4\right )} + 3 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )} \log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right )^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right ) + 12 \, x}{3 \, {\left (x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \left (x\right ) + 4 \, x\right )}} \,d x } \]

[In]

integrate(((12*exp(exp(-7/3*x+4))+112*x*exp(-7/3*x+4))*log((20*log(x)^2*exp(exp(-7/3*x+4))^2+160*log(x)*exp(ex
p(-7/3*x+4))+320)/exp(exp(-7/3*x+4))^2)+3*x*log(x)*exp(exp(-7/3*x+4))+12*x)/(3*x*log(x)*exp(exp(-7/3*x+4))+12*
x),x, algorithm="giac")

[Out]

integrate(1/3*(3*x*e^(e^(-7/3*x + 4))*log(x) + 4*(28*x*e^(-7/3*x + 4) + 3*e^(e^(-7/3*x + 4)))*log(20*(e^(2*e^(
-7/3*x + 4))*log(x)^2 + 8*e^(e^(-7/3*x + 4))*log(x) + 16)*e^(-2*e^(-7/3*x + 4))) + 12*x)/(x*e^(e^(-7/3*x + 4))
*log(x) + 4*x), x)

Mupad [B] (verification not implemented)

Time = 10.05 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx={\ln \left (20\,{\ln \left (x\right )}^2+160\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4}{{\left ({\mathrm {e}}^x\right )}^{7/3}}}\,\ln \left (x\right )+320\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^4}{{\left ({\mathrm {e}}^x\right )}^{7/3}}}\right )}^2+x \]

[In]

int((12*x + log(exp(-2*exp(4 - (7*x)/3))*(20*exp(2*exp(4 - (7*x)/3))*log(x)^2 + 160*exp(exp(4 - (7*x)/3))*log(
x) + 320))*(12*exp(exp(4 - (7*x)/3)) + 112*x*exp(4 - (7*x)/3)) + 3*x*exp(exp(4 - (7*x)/3))*log(x))/(12*x + 3*x
*exp(exp(4 - (7*x)/3))*log(x)),x)

[Out]

x + log(320*exp(-(2*exp(4))/exp(x)^(7/3)) + 20*log(x)^2 + 160*exp(-exp(4)/exp(x)^(7/3))*log(x))^2