\(\int \frac {-e^{360 x^2-120 x^3+10 x^4} x+(e^{360 x^2-120 x^3+10 x^4} (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5)+e^{360 x^2-120 x^3+10 x^4} (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5) \log (2-x)) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx\) [3535]

Optimal result

Integrand size = 154, antiderivative size = 25 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \]

[Out]

exp(10*x^2*(-6+x)^2)/ln(ln(2-x)+2)*x

Rubi [F]

\[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx \]

[In]

Int[(-(E^(360*x^2 - 120*x^3 + 10*x^4)*x) + (E^(360*x^2 - 120*x^3 + 10*x^4)*(-4 + 2*x - 2880*x^2 + 2880*x^3 - 8
80*x^4 + 80*x^5) + E^(360*x^2 - 120*x^3 + 10*x^4)*(-2 + x - 1440*x^2 + 1440*x^3 - 440*x^4 + 40*x^5)*Log[2 - x]
)*Log[2 + Log[2 - x]])/((-4 + 2*x + (-2 + x)*Log[2 - x])*Log[2 + Log[2 - x]]^2),x]

[Out]

-Defer[Int][E^(10*(-6 + x)^2*x^2)/((2 + Log[2 - x])*Log[2 + Log[2 - x]]^2), x] - 2*Defer[Int][E^(10*(-6 + x)^2
*x^2)/((-2 + x)*(2 + Log[2 - x])*Log[2 + Log[2 - x]]^2), x] + Defer[Int][E^(10*(-6 + x)^2*x^2)/Log[2 + Log[2 -
x]], x] + 720*Defer[Int][(E^(10*(-6 + x)^2*x^2)*x^2)/Log[2 + Log[2 - x]], x] - 360*Defer[Int][(E^(10*(-6 + x)
^2*x^2)*x^3)/Log[2 + Log[2 - x]], x] + 40*Defer[Int][(E^(10*(-6 + x)^2*x^2)*x^4)/Log[2 + Log[2 - x]], x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{10 (-6+x)^2 x^2} \left (x-\left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) (2+\log (2-x)) \log (2+\log (2-x))\right )}{(2-x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx \\ & = \int \left (-\frac {e^{10 (-6+x)^2 x^2} x}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))}+\frac {e^{10 (-6+x)^2 x^2} \left (1+720 x^2-360 x^3+40 x^4\right )}{\log (2+\log (2-x))}\right ) \, dx \\ & = -\int \frac {e^{10 (-6+x)^2 x^2} x}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx+\int \frac {e^{10 (-6+x)^2 x^2} \left (1+720 x^2-360 x^3+40 x^4\right )}{\log (2+\log (2-x))} \, dx \\ & = -\int \left (\frac {e^{10 (-6+x)^2 x^2}}{(2+\log (2-x)) \log ^2(2+\log (2-x))}+\frac {2 e^{10 (-6+x)^2 x^2}}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))}\right ) \, dx+\int \left (\frac {e^{10 (-6+x)^2 x^2}}{\log (2+\log (2-x))}+\frac {720 e^{10 (-6+x)^2 x^2} x^2}{\log (2+\log (2-x))}-\frac {360 e^{10 (-6+x)^2 x^2} x^3}{\log (2+\log (2-x))}+\frac {40 e^{10 (-6+x)^2 x^2} x^4}{\log (2+\log (2-x))}\right ) \, dx \\ & = -\left (2 \int \frac {e^{10 (-6+x)^2 x^2}}{(-2+x) (2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx\right )+40 \int \frac {e^{10 (-6+x)^2 x^2} x^4}{\log (2+\log (2-x))} \, dx-360 \int \frac {e^{10 (-6+x)^2 x^2} x^3}{\log (2+\log (2-x))} \, dx+720 \int \frac {e^{10 (-6+x)^2 x^2} x^2}{\log (2+\log (2-x))} \, dx-\int \frac {e^{10 (-6+x)^2 x^2}}{(2+\log (2-x)) \log ^2(2+\log (2-x))} \, dx+\int \frac {e^{10 (-6+x)^2 x^2}}{\log (2+\log (2-x))} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \]

[In]

Integrate[(-(E^(360*x^2 - 120*x^3 + 10*x^4)*x) + (E^(360*x^2 - 120*x^3 + 10*x^4)*(-4 + 2*x - 2880*x^2 + 2880*x
^3 - 880*x^4 + 80*x^5) + E^(360*x^2 - 120*x^3 + 10*x^4)*(-2 + x - 1440*x^2 + 1440*x^3 - 440*x^4 + 40*x^5)*Log[
2 - x])*Log[2 + Log[2 - x]])/((-4 + 2*x + (-2 + x)*Log[2 - x])*Log[2 + Log[2 - x]]^2),x]

[Out]

(E^(10*(-6 + x)^2*x^2)*x)/Log[2 + Log[2 - x]]

Maple [A] (verified)

Time = 7.92 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00

method	result	size
risch	\(\frac {{\mathrm e}^{10 x^{2} \left (-6+x \right )^{2}} x}{\ln \left (\ln \left (2-x \right )+2\right )}\)	\(25\)
parallelrisch	\(\frac {x \,{\mathrm e}^{10 x^{4}-120 x^{3}+360 x^{2}}}{\ln \left (\ln \left (2-x \right )+2\right )}\)	\(31\)

[In]

int((((40*x^5-440*x^4+1440*x^3-1440*x^2+x-2)*exp(10*x^4-120*x^3+360*x^2)*ln(2-x)+(80*x^5-880*x^4+2880*x^3-2880
*x^2+2*x-4)*exp(10*x^4-120*x^3+360*x^2))*ln(ln(2-x)+2)-x*exp(10*x^4-120*x^3+360*x^2))/((-2+x)*ln(2-x)+2*x-4)/l
n(ln(2-x)+2)^2,x,method=_RETURNVERBOSE)

[Out]

exp(10*x^2*(-6+x)^2)/ln(ln(2-x)+2)*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \]

[In]

integrate((((40*x^5-440*x^4+1440*x^3-1440*x^2+x-2)*exp(10*x^4-120*x^3+360*x^2)*log(2-x)+(80*x^5-880*x^4+2880*x
^3-2880*x^2+2*x-4)*exp(10*x^4-120*x^3+360*x^2))*log(log(2-x)+2)-x*exp(10*x^4-120*x^3+360*x^2))/((-2+x)*log(2-x
)+2*x-4)/log(log(2-x)+2)^2,x, algorithm="fricas")

[Out]

x*e^(10*x^4 - 120*x^3 + 360*x^2)/log(log(-x + 2) + 2)

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {x e^{10 x^{4} - 120 x^{3} + 360 x^{2}}}{\log {\left (\log {\left (2 - x \right )} + 2 \right )}} \]

[In]

integrate((((40*x**5-440*x**4+1440*x**3-1440*x**2+x-2)*exp(10*x**4-120*x**3+360*x**2)*ln(2-x)+(80*x**5-880*x**
4+2880*x**3-2880*x**2+2*x-4)*exp(10*x**4-120*x**3+360*x**2))*ln(ln(2-x)+2)-x*exp(10*x**4-120*x**3+360*x**2))/(
(-2+x)*ln(2-x)+2*x-4)/ln(ln(2-x)+2)**2,x)

[Out]

x*exp(10*x**4 - 120*x**3 + 360*x**2)/log(log(2 - x) + 2)

Maxima [A] (verification not implemented)

none

Time = 0.34 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \]

[In]

integrate((((40*x^5-440*x^4+1440*x^3-1440*x^2+x-2)*exp(10*x^4-120*x^3+360*x^2)*log(2-x)+(80*x^5-880*x^4+2880*x
^3-2880*x^2+2*x-4)*exp(10*x^4-120*x^3+360*x^2))*log(log(2-x)+2)-x*exp(10*x^4-120*x^3+360*x^2))/((-2+x)*log(2-x
)+2*x-4)/log(log(2-x)+2)^2,x, algorithm="maxima")

[Out]

x*e^(10*x^4 - 120*x^3 + 360*x^2)/log(log(-x + 2) + 2)

Giac [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \]

[In]

integrate((((40*x^5-440*x^4+1440*x^3-1440*x^2+x-2)*exp(10*x^4-120*x^3+360*x^2)*log(2-x)+(80*x^5-880*x^4+2880*x
^3-2880*x^2+2*x-4)*exp(10*x^4-120*x^3+360*x^2))*log(log(2-x)+2)-x*exp(10*x^4-120*x^3+360*x^2))/((-2+x)*log(2-x
)+2*x-4)/log(log(2-x)+2)^2,x, algorithm="giac")

[Out]

x*e^(10*x^4 - 120*x^3 + 360*x^2)/log(log(-x + 2) + 2)

Mupad [B] (verification not implemented)

Time = 0.41 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int \frac {-e^{360 x^2-120 x^3+10 x^4} x+\left (e^{360 x^2-120 x^3+10 x^4} \left (-4+2 x-2880 x^2+2880 x^3-880 x^4+80 x^5\right )+e^{360 x^2-120 x^3+10 x^4} \left (-2+x-1440 x^2+1440 x^3-440 x^4+40 x^5\right ) \log (2-x)\right ) \log (2+\log (2-x))}{(-4+2 x+(-2+x) \log (2-x)) \log ^2(2+\log (2-x))} \, dx=\frac {x\,{\mathrm {e}}^{10\,x^4}\,{\mathrm {e}}^{-120\,x^3}\,{\mathrm {e}}^{360\,x^2}}{\ln \left (\ln \left (2-x\right )+2\right )} \]

[In]

int((log(log(2 - x) + 2)*(exp(360*x^2 - 120*x^3 + 10*x^4)*(2*x - 2880*x^2 + 2880*x^3 - 880*x^4 + 80*x^5 - 4) +
exp(360*x^2 - 120*x^3 + 10*x^4)*log(2 - x)*(x - 1440*x^2 + 1440*x^3 - 440*x^4 + 40*x^5 - 2)) - x*exp(360*x^2
- 120*x^3 + 10*x^4))/(log(log(2 - x) + 2)^2*(2*x + log(2 - x)*(x - 2) - 4)),x)

[Out]

(x*exp(10*x^4)*exp(-120*x^3)*exp(360*x^2))/log(log(2 - x) + 2)