3.101.35 \(\int e^{-2 x+e^{-2 x} (x^2+2 e^x x^3+e^{2 x} x^4+(-10 x^2-2 x^3+e^x (-10 x^3-2 x^4)) \log ^2(x)+(25 x^2+10 x^3+x^4) \log ^4(x))} (2 x-2 x^2+4 e^{2 x} x^3+e^x (6 x^2-2 x^3)+(-20 x-4 x^2+e^x (-20 x^2-4 x^3)) \log (x)+(-20 x+14 x^2+4 x^3+e^x (-30 x^2+2 x^3+2 x^4)) \log ^2(x)+(100 x+40 x^2+4 x^3) \log ^3(x)+(50 x-20 x^2-16 x^3-2 x^4) \log ^4(x)) \, dx\)

Optimal. Leaf size=27 \[ e^{x^2 \left (x-e^{-x} \left (-1+(5+x) \log ^2(x)\right )\right )^2} \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-2*x + (x^2 + 2*E^x*x^3 + E^(2*x)*x^4 + (-10*x^2 - 2*x^3 + E^x*(-10*x^3 - 2*x^4))*Log[x]^2 + (25*x^2 +
10*x^3 + x^4)*Log[x]^4)/E^(2*x))*(2*x - 2*x^2 + 4*E^(2*x)*x^3 + E^x*(6*x^2 - 2*x^3) + (-20*x - 4*x^2 + E^x*(-2
0*x^2 - 4*x^3))*Log[x] + (-20*x + 14*x^2 + 4*x^3 + E^x*(-30*x^2 + 2*x^3 + 2*x^4))*Log[x]^2 + (100*x + 40*x^2 +
4*x^3)*Log[x]^3 + (50*x - 20*x^2 - 16*x^3 - 2*x^4)*Log[x]^4),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.33, size = 29, normalized size = 1.07 \begin {gather*} e^{e^{-2 x} x^2 \left (1+e^x x-(5+x) \log ^2(x)\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-2*x + (x^2 + 2*E^x*x^3 + E^(2*x)*x^4 + (-10*x^2 - 2*x^3 + E^x*(-10*x^3 - 2*x^4))*Log[x]^2 + (25*
x^2 + 10*x^3 + x^4)*Log[x]^4)/E^(2*x))*(2*x - 2*x^2 + 4*E^(2*x)*x^3 + E^x*(6*x^2 - 2*x^3) + (-20*x - 4*x^2 + E
^x*(-20*x^2 - 4*x^3))*Log[x] + (-20*x + 14*x^2 + 4*x^3 + E^x*(-30*x^2 + 2*x^3 + 2*x^4))*Log[x]^2 + (100*x + 40
*x^2 + 4*x^3)*Log[x]^3 + (50*x - 20*x^2 - 16*x^3 - 2*x^4)*Log[x]^4),x]

[Out]

E^((x^2*(1 + E^x*x - (5 + x)*Log[x]^2)^2)/E^(2*x))

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fricas [B]  time = 2.30, size = 79, normalized size = 2.93 \begin {gather*} e^{\left ({\left ({\left (x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )} \log \relax (x)^{4} + 2 \, x^{3} e^{x} - 2 \, {\left (x^{3} + 5 \, x^{2} + {\left (x^{4} + 5 \, x^{3}\right )} e^{x}\right )} \log \relax (x)^{2} + x^{2} + {\left (x^{4} - 2 \, x\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-2 \, x\right )} + 2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^4-16*x^3-20*x^2+50*x)*log(x)^4+(4*x^3+40*x^2+100*x)*log(x)^3+((2*x^4+2*x^3-30*x^2)*exp(x)+4*x
^3+14*x^2-20*x)*log(x)^2+((-4*x^3-20*x^2)*exp(x)-4*x^2-20*x)*log(x)+4*exp(x)^2*x^3+(-2*x^3+6*x^2)*exp(x)-2*x^2
+2*x)*exp(((x^4+10*x^3+25*x^2)*log(x)^4+((-2*x^4-10*x^3)*exp(x)-2*x^3-10*x^2)*log(x)^2+exp(x)^2*x^4+2*exp(x)*x
^3+x^2)/exp(x)^2)/exp(x)^2,x, algorithm="fricas")

[Out]

e^(((x^4 + 10*x^3 + 25*x^2)*log(x)^4 + 2*x^3*e^x - 2*(x^3 + 5*x^2 + (x^4 + 5*x^3)*e^x)*log(x)^2 + x^2 + (x^4 -
2*x)*e^(2*x))*e^(-2*x) + 2*x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -2 \, {\left ({\left (x^{4} + 8 \, x^{3} + 10 \, x^{2} - 25 \, x\right )} \log \relax (x)^{4} - 2 \, x^{3} e^{\left (2 \, x\right )} - 2 \, {\left (x^{3} + 10 \, x^{2} + 25 \, x\right )} \log \relax (x)^{3} - {\left (2 \, x^{3} + 7 \, x^{2} + {\left (x^{4} + x^{3} - 15 \, x^{2}\right )} e^{x} - 10 \, x\right )} \log \relax (x)^{2} + x^{2} + {\left (x^{3} - 3 \, x^{2}\right )} e^{x} + 2 \, {\left (x^{2} + {\left (x^{3} + 5 \, x^{2}\right )} e^{x} + 5 \, x\right )} \log \relax (x) - x\right )} e^{\left ({\left (x^{4} e^{\left (2 \, x\right )} + {\left (x^{4} + 10 \, x^{3} + 25 \, x^{2}\right )} \log \relax (x)^{4} + 2 \, x^{3} e^{x} - 2 \, {\left (x^{3} + 5 \, x^{2} + {\left (x^{4} + 5 \, x^{3}\right )} e^{x}\right )} \log \relax (x)^{2} + x^{2}\right )} e^{\left (-2 \, x\right )} - 2 \, x\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^4-16*x^3-20*x^2+50*x)*log(x)^4+(4*x^3+40*x^2+100*x)*log(x)^3+((2*x^4+2*x^3-30*x^2)*exp(x)+4*x
^3+14*x^2-20*x)*log(x)^2+((-4*x^3-20*x^2)*exp(x)-4*x^2-20*x)*log(x)+4*exp(x)^2*x^3+(-2*x^3+6*x^2)*exp(x)-2*x^2
+2*x)*exp(((x^4+10*x^3+25*x^2)*log(x)^4+((-2*x^4-10*x^3)*exp(x)-2*x^3-10*x^2)*log(x)^2+exp(x)^2*x^4+2*exp(x)*x
^3+x^2)/exp(x)^2)/exp(x)^2,x, algorithm="giac")

[Out]

integrate(-2*((x^4 + 8*x^3 + 10*x^2 - 25*x)*log(x)^4 - 2*x^3*e^(2*x) - 2*(x^3 + 10*x^2 + 25*x)*log(x)^3 - (2*x
^3 + 7*x^2 + (x^4 + x^3 - 15*x^2)*e^x - 10*x)*log(x)^2 + x^2 + (x^3 - 3*x^2)*e^x + 2*(x^2 + (x^3 + 5*x^2)*e^x
+ 5*x)*log(x) - x)*e^((x^4*e^(2*x) + (x^4 + 10*x^3 + 25*x^2)*log(x)^4 + 2*x^3*e^x - 2*(x^3 + 5*x^2 + (x^4 + 5*
x^3)*e^x)*log(x)^2 + x^2)*e^(-2*x) - 2*x), x)

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maple [B]  time = 0.13, size = 82, normalized size = 3.04

method	result	size
risch	\({\mathrm e}^{-x^{2} \left (-x^{2} \ln \relax (x )^{4}-10 x \ln \relax (x )^{4}+2 x^{2} {\mathrm e}^{x} \ln \relax (x )^{2}-25 \ln \relax (x )^{4}+10 x \,{\mathrm e}^{x} \ln \relax (x )^{2}+2 x \ln \relax (x )^{2}-{\mathrm e}^{2 x} x^{2}+10 \ln \relax (x )^{2}-2 \,{\mathrm e}^{x} x -1\right ) {\mathrm e}^{-2 x}}\)	\(82\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^4-16*x^3-20*x^2+50*x)*ln(x)^4+(4*x^3+40*x^2+100*x)*ln(x)^3+((2*x^4+2*x^3-30*x^2)*exp(x)+4*x^3+14*x^
2-20*x)*ln(x)^2+((-4*x^3-20*x^2)*exp(x)-4*x^2-20*x)*ln(x)+4*exp(x)^2*x^3+(-2*x^3+6*x^2)*exp(x)-2*x^2+2*x)*exp(
((x^4+10*x^3+25*x^2)*ln(x)^4+((-2*x^4-10*x^3)*exp(x)-2*x^3-10*x^2)*ln(x)^2+exp(x)^2*x^4+2*exp(x)*x^3+x^2)/exp(
x)^2)/exp(x)^2,x,method=_RETURNVERBOSE)

[Out]

exp(-x^2*(-x^2*ln(x)^4-10*x*ln(x)^4+2*x^2*exp(x)*ln(x)^2-25*ln(x)^4+10*x*exp(x)*ln(x)^2+2*x*ln(x)^2-exp(2*x)*x
^2+10*ln(x)^2-2*exp(x)*x-1)*exp(-2*x))

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maxima [B]  time = 0.90, size = 112, normalized size = 4.15 \begin {gather*} e^{\left (x^{4} e^{\left (-2 \, x\right )} \log \relax (x)^{4} + 10 \, x^{3} e^{\left (-2 \, x\right )} \log \relax (x)^{4} - 2 \, x^{4} e^{\left (-x\right )} \log \relax (x)^{2} + 25 \, x^{2} e^{\left (-2 \, x\right )} \log \relax (x)^{4} - 10 \, x^{3} e^{\left (-x\right )} \log \relax (x)^{2} - 2 \, x^{3} e^{\left (-2 \, x\right )} \log \relax (x)^{2} - 10 \, x^{2} e^{\left (-2 \, x\right )} \log \relax (x)^{2} + x^{4} + 2 \, x^{3} e^{\left (-x\right )} + x^{2} e^{\left (-2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^4-16*x^3-20*x^2+50*x)*log(x)^4+(4*x^3+40*x^2+100*x)*log(x)^3+((2*x^4+2*x^3-30*x^2)*exp(x)+4*x
^3+14*x^2-20*x)*log(x)^2+((-4*x^3-20*x^2)*exp(x)-4*x^2-20*x)*log(x)+4*exp(x)^2*x^3+(-2*x^3+6*x^2)*exp(x)-2*x^2
+2*x)*exp(((x^4+10*x^3+25*x^2)*log(x)^4+((-2*x^4-10*x^3)*exp(x)-2*x^3-10*x^2)*log(x)^2+exp(x)^2*x^4+2*exp(x)*x
^3+x^2)/exp(x)^2)/exp(x)^2,x, algorithm="maxima")

[Out]

e^(x^4*e^(-2*x)*log(x)^4 + 10*x^3*e^(-2*x)*log(x)^4 - 2*x^4*e^(-x)*log(x)^2 + 25*x^2*e^(-2*x)*log(x)^4 - 10*x^
3*e^(-x)*log(x)^2 - 2*x^3*e^(-2*x)*log(x)^2 - 10*x^2*e^(-2*x)*log(x)^2 + x^4 + 2*x^3*e^(-x) + x^2*e^(-2*x))

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mupad [B]  time = 7.92, size = 121, normalized size = 4.48 \begin {gather*} {\mathrm {e}}^{-2\,x^3\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{-x}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^4}\,{\mathrm {e}}^{-10\,x^2\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-10\,x^3\,{\mathrm {e}}^{-x}\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{10\,x^3\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^4}\,{\mathrm {e}}^{25\,x^2\,{\mathrm {e}}^{-2\,x}\,{\ln \relax (x)}^4}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{2\,x^3\,{\mathrm {e}}^{-x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-2*x)*exp(exp(-2*x)*(2*x^3*exp(x) + log(x)^4*(25*x^2 + 10*x^3 + x^4) + x^4*exp(2*x) - log(x)^2*(exp(x)
*(10*x^3 + 2*x^4) + 10*x^2 + 2*x^3) + x^2))*(2*x + exp(x)*(6*x^2 - 2*x^3) + log(x)^3*(100*x + 40*x^2 + 4*x^3)
+ 4*x^3*exp(2*x) - log(x)^4*(20*x^2 - 50*x + 16*x^3 + 2*x^4) + log(x)^2*(exp(x)*(2*x^3 - 30*x^2 + 2*x^4) - 20*
x + 14*x^2 + 4*x^3) - log(x)*(20*x + exp(x)*(20*x^2 + 4*x^3) + 4*x^2) - 2*x^2),x)

[Out]

exp(-2*x^3*exp(-2*x)*log(x)^2)*exp(-2*x^4*exp(-x)*log(x)^2)*exp(x^4*exp(-2*x)*log(x)^4)*exp(-10*x^2*exp(-2*x)*
log(x)^2)*exp(-10*x^3*exp(-x)*log(x)^2)*exp(10*x^3*exp(-2*x)*log(x)^4)*exp(25*x^2*exp(-2*x)*log(x)^4)*exp(x^4)
*exp(x^2*exp(-2*x))*exp(2*x^3*exp(-x))

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sympy [B]  time = 1.71, size = 75, normalized size = 2.78 \begin {gather*} e^{\left (x^{4} e^{2 x} + 2 x^{3} e^{x} + x^{2} + \left (- 2 x^{3} - 10 x^{2} + \left (- 2 x^{4} - 10 x^{3}\right ) e^{x}\right ) \log {\relax (x )}^{2} + \left (x^{4} + 10 x^{3} + 25 x^{2}\right ) \log {\relax (x )}^{4}\right ) e^{- 2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**4-16*x**3-20*x**2+50*x)*ln(x)**4+(4*x**3+40*x**2+100*x)*ln(x)**3+((2*x**4+2*x**3-30*x**2)*ex
p(x)+4*x**3+14*x**2-20*x)*ln(x)**2+((-4*x**3-20*x**2)*exp(x)-4*x**2-20*x)*ln(x)+4*exp(x)**2*x**3+(-2*x**3+6*x*
*2)*exp(x)-2*x**2+2*x)*exp(((x**4+10*x**3+25*x**2)*ln(x)**4+((-2*x**4-10*x**3)*exp(x)-2*x**3-10*x**2)*ln(x)**2
+exp(x)**2*x**4+2*exp(x)*x**3+x**2)/exp(x)**2)/exp(x)**2,x)

[Out]

exp((x**4*exp(2*x) + 2*x**3*exp(x) + x**2 + (-2*x**3 - 10*x**2 + (-2*x**4 - 10*x**3)*exp(x))*log(x)**2 + (x**4
+ 10*x**3 + 25*x**2)*log(x)**4)*exp(-2*x))

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