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

Optimal. Leaf size=25 \[ \frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \]

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Rubi [F]  time = 3.09, 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 {-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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 25, normalized size = 1.00 \begin {gather*} \frac {e^{10 (-6+x)^2 x^2} x}{\log (2+\log (2-x))} \end {gather*}

Antiderivative was successfully verified.

[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]]

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fricas [A]  time = 0.46, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))/((x-2)*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)

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giac [A]  time = 0.32, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))/((x-2)*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)

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maple [A]  time = 0.04, size = 25, normalized size = 1.00

method	result	size
risch	\(\frac {{\mathrm e}^{10 x^{2} \left (x -6\right )^{2}} x}{\ln \left (\ln \left (2-x \right )+2\right )}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[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))/((x-2)*ln(2-x)+2*x-4)/ln
(ln(2-x)+2)^2,x,method=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.60, size = 30, normalized size = 1.20 \begin {gather*} \frac {x e^{\left (10 \, x^{4} - 120 \, x^{3} + 360 \, x^{2}\right )}}{\log \left (\log \left (-x + 2\right ) + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))/((x-2)*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)

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mupad [B]  time = 0.38, size = 31, normalized size = 1.24 \begin {gather*} \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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [A]  time = 0.58, size = 26, normalized size = 1.04 \begin {gather*} \frac {x e^{10 x^{4} - 120 x^{3} + 360 x^{2}}}{\log {\left (\log {\left (2 - x \right )} + 2 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))/(
(x-2)*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)

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