3.10.87 \(\int \frac {32 x^4-16 x^5+2 x^6+(-16 x^3+4 x^4) \log (x)+2 x^2 \log ^2(x)+e^{\frac {-5 x+4 x^3-x^3 \log (x)}{-4 x+x^2+\log (x)}} (10 x^2+2 x^4-56 x^5+6 x^6+(-10 x^2+24 x^4+16 x^5-2 x^6) \log (x)-6 x^4 \log ^2(x))+e^{\frac {2 (-5 x+4 x^3-x^3 \log (x))}{-4 x+x^2+\log (x)}} (10 x-16 x^2+10 x^3-57 x^4+6 x^5+(-2 x-2 x^2+24 x^3+16 x^4-2 x^5) \log (x)+(-1-6 x^3) \log ^2(x))}{16 x^4-8 x^5+x^6+(-8 x^3+2 x^4) \log (x)+x^2 \log ^2(x)} \, dx\)

Optimal. Leaf size=36 \[ x+\frac {\left (e^{\frac {-5+x^2 (4-\log (x))}{-4+x+\frac {\log (x)}{x}}}+x\right )^2}{x} \]

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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[(32*x^4 - 16*x^5 + 2*x^6 + (-16*x^3 + 4*x^4)*Log[x] + 2*x^2*Log[x]^2 + E^((-5*x + 4*x^3 - x^3*Log[x])/(-4*
x + x^2 + Log[x]))*(10*x^2 + 2*x^4 - 56*x^5 + 6*x^6 + (-10*x^2 + 24*x^4 + 16*x^5 - 2*x^6)*Log[x] - 6*x^4*Log[x
]^2) + E^((2*(-5*x + 4*x^3 - x^3*Log[x]))/(-4*x + x^2 + Log[x]))*(10*x - 16*x^2 + 10*x^3 - 57*x^4 + 6*x^5 + (-
2*x - 2*x^2 + 24*x^3 + 16*x^4 - 2*x^5)*Log[x] + (-1 - 6*x^3)*Log[x]^2))/(16*x^4 - 8*x^5 + x^6 + (-8*x^3 + 2*x^
4)*Log[x] + x^2*Log[x]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.32, size = 66, normalized size = 1.83 \begin {gather*} 2 e^{-\frac {x \left (5-4 x^2+x^2 \log (x)\right )}{(-4+x) x+\log (x)}}+\frac {e^{-\frac {2 x \left (5-4 x^2+x^2 \log (x)\right )}{(-4+x) x+\log (x)}}}{x}+2 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(32*x^4 - 16*x^5 + 2*x^6 + (-16*x^3 + 4*x^4)*Log[x] + 2*x^2*Log[x]^2 + E^((-5*x + 4*x^3 - x^3*Log[x]
)/(-4*x + x^2 + Log[x]))*(10*x^2 + 2*x^4 - 56*x^5 + 6*x^6 + (-10*x^2 + 24*x^4 + 16*x^5 - 2*x^6)*Log[x] - 6*x^4
*Log[x]^2) + E^((2*(-5*x + 4*x^3 - x^3*Log[x]))/(-4*x + x^2 + Log[x]))*(10*x - 16*x^2 + 10*x^3 - 57*x^4 + 6*x^
5 + (-2*x - 2*x^2 + 24*x^3 + 16*x^4 - 2*x^5)*Log[x] + (-1 - 6*x^3)*Log[x]^2))/(16*x^4 - 8*x^5 + x^6 + (-8*x^3
+ 2*x^4)*Log[x] + x^2*Log[x]^2),x]

[Out]

2/E^((x*(5 - 4*x^2 + x^2*Log[x]))/((-4 + x)*x + Log[x])) + 1/(E^((2*x*(5 - 4*x^2 + x^2*Log[x]))/((-4 + x)*x +
Log[x]))*x) + 2*x

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fricas [B]  time = 0.90, size = 71, normalized size = 1.97 \begin {gather*} \frac {2 \, x^{2} + 2 \, x e^{\left (-\frac {x^{3} \log \relax (x) - 4 \, x^{3} + 5 \, x}{x^{2} - 4 \, x + \log \relax (x)}\right )} + e^{\left (-\frac {2 \, {\left (x^{3} \log \relax (x) - 4 \, x^{3} + 5 \, x\right )}}{x^{2} - 4 \, x + \log \relax (x)}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 4.89, size = 71, normalized size = 1.97 \begin {gather*} \frac {2 \, x^{2} + 2 \, x e^{\left (-\frac {x^{3} \log \relax (x) - 4 \, x^{3} + 5 \, x}{x^{2} - 4 \, x + \log \relax (x)}\right )} + e^{\left (-\frac {2 \, {\left (x^{3} \log \relax (x) - 4 \, x^{3} + 5 \, x\right )}}{x^{2} - 4 \, x + \log \relax (x)}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.07, size = 67, normalized size = 1.86

method	result	size
risch	\(2 x +\frac {{\mathrm e}^{-\frac {2 x \left (x^{2} \ln \relax (x )-4 x^{2}+5\right )}{\ln \relax (x )+x^{2}-4 x}}}{x}+2 \,{\mathrm e}^{-\frac {x \left (x^{2} \ln \relax (x )-4 x^{2}+5\right )}{\ln \relax (x )+x^{2}-4 x}}\)	\(67\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-6*x^3-1)*ln(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*ln(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((-x^3*ln(
x)+4*x^3-5*x)/(ln(x)+x^2-4*x))^2+(-6*x^4*ln(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*ln(x)+6*x^6-56*x^5+2*x^4+10*x^2
)*exp((-x^3*ln(x)+4*x^3-5*x)/(ln(x)+x^2-4*x))+2*x^2*ln(x)^2+(4*x^4-16*x^3)*ln(x)+2*x^6-16*x^5+32*x^4)/(x^2*ln(
x)^2+(2*x^4-8*x^3)*ln(x)+x^6-8*x^5+16*x^4),x,method=_RETURNVERBOSE)

[Out]

2*x+1/x*exp(-2*x*(x^2*ln(x)-4*x^2+5)/(ln(x)+x^2-4*x))+2*exp(-x*(x^2*ln(x)-4*x^2+5)/(ln(x)+x^2-4*x))

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maxima [B]  time = 0.77, size = 235, normalized size = 6.53 \begin {gather*} \frac {{\left (2 \, x^{10} e^{\left (2 \, x \log \relax (x) + \frac {40 \, x \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)} + \frac {32 \, \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)}\right )} + 2 \, x^{5} e^{\left (x \log \relax (x) + \frac {x \log \relax (x)^{2}}{x^{2} - 4 \, x + \log \relax (x)} + 4 \, x + \frac {20 \, x \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)} + \frac {4 \, \log \relax (x)^{2}}{x^{2} - 4 \, x + \log \relax (x)} + \frac {59 \, x}{x^{2} - 4 \, x + \log \relax (x)} + \frac {16 \, \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)} + 16\right )} + e^{\left (\frac {2 \, x \log \relax (x)^{2}}{x^{2} - 4 \, x + \log \relax (x)} + 8 \, x + \frac {8 \, \log \relax (x)^{2}}{x^{2} - 4 \, x + \log \relax (x)} + \frac {118 \, x}{x^{2} - 4 \, x + \log \relax (x)} + 32\right )}\right )} e^{\left (-2 \, x \log \relax (x) - \frac {40 \, x \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)} - \frac {32 \, \log \relax (x)}{x^{2} - 4 \, x + \log \relax (x)}\right )}}{x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x^3-1)*log(x)^2+(-2*x^5+16*x^4+24*x^3-2*x^2-2*x)*log(x)+6*x^5-57*x^4+10*x^3-16*x^2+10*x)*exp((
-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))^2+(-6*x^4*log(x)^2+(-2*x^6+16*x^5+24*x^4-10*x^2)*log(x)+6*x^6-56*x^5+
2*x^4+10*x^2)*exp((-x^3*log(x)+4*x^3-5*x)/(log(x)+x^2-4*x))+2*x^2*log(x)^2+(4*x^4-16*x^3)*log(x)+2*x^6-16*x^5+
32*x^4)/(x^2*log(x)^2+(2*x^4-8*x^3)*log(x)+x^6-8*x^5+16*x^4),x, algorithm="maxima")

[Out]

(2*x^10*e^(2*x*log(x) + 40*x*log(x)/(x^2 - 4*x + log(x)) + 32*log(x)/(x^2 - 4*x + log(x))) + 2*x^5*e^(x*log(x)
+ x*log(x)^2/(x^2 - 4*x + log(x)) + 4*x + 20*x*log(x)/(x^2 - 4*x + log(x)) + 4*log(x)^2/(x^2 - 4*x + log(x))
+ 59*x/(x^2 - 4*x + log(x)) + 16*log(x)/(x^2 - 4*x + log(x)) + 16) + e^(2*x*log(x)^2/(x^2 - 4*x + log(x)) + 8*
x + 8*log(x)^2/(x^2 - 4*x + log(x)) + 118*x/(x^2 - 4*x + log(x)) + 32))*e^(-2*x*log(x) - 40*x*log(x)/(x^2 - 4*
x + log(x)) - 32*log(x)/(x^2 - 4*x + log(x)))/x^9

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mupad [B]  time = 1.30, size = 113, normalized size = 3.14 \begin {gather*} 2\,x+\frac {2\,{\mathrm {e}}^{-\frac {5\,x}{\ln \relax (x)-4\,x+x^2}}\,{\mathrm {e}}^{\frac {4\,x^3}{\ln \relax (x)-4\,x+x^2}}}{x^{\frac {x^3}{\ln \relax (x)-4\,x+x^2}}}+\frac {{\mathrm {e}}^{-\frac {10\,x}{\ln \relax (x)-4\,x+x^2}}\,{\mathrm {e}}^{\frac {8\,x^3}{\ln \relax (x)-4\,x+x^2}}}{x^{\frac {2\,x^3}{\ln \relax (x)-4\,x+x^2}}\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)*(16*x^3 - 4*x^4) + exp(-(5*x + x^3*log(x) - 4*x^3)/(log(x) - 4*x + x^2))*(6*x^4*log(x)^2 + log(x)
*(10*x^2 - 24*x^4 - 16*x^5 + 2*x^6) - 10*x^2 - 2*x^4 + 56*x^5 - 6*x^6) - 2*x^2*log(x)^2 + exp(-(2*(5*x + x^3*l
og(x) - 4*x^3))/(log(x) - 4*x + x^2))*(log(x)^2*(6*x^3 + 1) - 10*x + log(x)*(2*x + 2*x^2 - 24*x^3 - 16*x^4 + 2
*x^5) + 16*x^2 - 10*x^3 + 57*x^4 - 6*x^5) - 32*x^4 + 16*x^5 - 2*x^6)/(x^2*log(x)^2 - log(x)*(8*x^3 - 2*x^4) +
16*x^4 - 8*x^5 + x^6),x)

[Out]

2*x + (2*exp(-(5*x)/(log(x) - 4*x + x^2))*exp((4*x^3)/(log(x) - 4*x + x^2)))/x^(x^3/(log(x) - 4*x + x^2)) + (e
xp(-(10*x)/(log(x) - 4*x + x^2))*exp((8*x^3)/(log(x) - 4*x + x^2)))/(x^((2*x^3)/(log(x) - 4*x + x^2))*x)

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sympy [B]  time = 0.77, size = 63, normalized size = 1.75 \begin {gather*} 2 x + \frac {2 x e^{\frac {- x^{3} \log {\relax (x )} + 4 x^{3} - 5 x}{x^{2} - 4 x + \log {\relax (x )}}} + e^{\frac {2 \left (- x^{3} \log {\relax (x )} + 4 x^{3} - 5 x\right )}{x^{2} - 4 x + \log {\relax (x )}}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-6*x**3-1)*ln(x)**2+(-2*x**5+16*x**4+24*x**3-2*x**2-2*x)*ln(x)+6*x**5-57*x**4+10*x**3-16*x**2+10*
x)*exp((-x**3*ln(x)+4*x**3-5*x)/(ln(x)+x**2-4*x))**2+(-6*x**4*ln(x)**2+(-2*x**6+16*x**5+24*x**4-10*x**2)*ln(x)
+6*x**6-56*x**5+2*x**4+10*x**2)*exp((-x**3*ln(x)+4*x**3-5*x)/(ln(x)+x**2-4*x))+2*x**2*ln(x)**2+(4*x**4-16*x**3
)*ln(x)+2*x**6-16*x**5+32*x**4)/(x**2*ln(x)**2+(2*x**4-8*x**3)*ln(x)+x**6-8*x**5+16*x**4),x)

[Out]

2*x + (2*x*exp((-x**3*log(x) + 4*x**3 - 5*x)/(x**2 - 4*x + log(x))) + exp(2*(-x**3*log(x) + 4*x**3 - 5*x)/(x**
2 - 4*x + log(x))))/x

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