3.88.86 \(\int \frac {4 x+e^{-8 x^3-2 x^4+2 (4 x^2+x^3) \log (x)} (16 x-44 x^2-16 x^3+(32 x+12 x^2) \log (x))+e^{-4 x^3-x^4+(4 x^2+x^3) \log (x)} (4+16 x^2-44 x^3-16 x^4+(32 x^2+12 x^3) \log (x))}{(5+e^{-8 x^3-2 x^4+2 (4 x^2+x^3) \log (x)}+2 e^{-4 x^3-x^4+(4 x^2+x^3) \log (x)} x+x^2) \log (5+e^{-8 x^3-2 x^4+2 (4 x^2+x^3) \log (x)}+2 e^{-4 x^3-x^4+(4 x^2+x^3) \log (x)} x+x^2) \log (\log (5+e^{-8 x^3-2 x^4+2 (4 x^2+x^3) \log (x)}+2 e^{-4 x^3-x^4+(4 x^2+x^3) \log (x)} x+x^2))} \, dx\) [8786]

Optimal. Leaf size=26 \[ \log \left (\log ^2\left (\log \left (5+\left (e^{x^2 (4+x) (-x+\log (x))}+x\right )^2\right )\right )\right ) \]

[Out]

ln(ln(ln(5+(exp((ln(x)-x)*x^2*(4+x))+x)^2))^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[(4*x + E^(-8*x^3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x])*(16*x - 44*x^2 - 16*x^3 + (32*x + 12*x^2)*Log[x]) + E^(
-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*(4 + 16*x^2 - 44*x^3 - 16*x^4 + (32*x^2 + 12*x^3)*Log[x]))/((5 + E^(-8*x^
3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2)*Log[5 + E^(-8*x^3 - 2
*x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2]*Log[Log[5 + E^(-8*x^3 - 2*
x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2]]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(60\) vs. \(2(26)=52\).
time = 0.52, size = 60, normalized size = 2.31 \begin {gather*} 2 \log \left (\log \left (\log \left (5+x^2+e^{-8 x^3-2 x^4} x^{2 x^2 (4+x)}+2 e^{-4 x^3-x^4} x^{1+x^2 (4+x)}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*x + E^(-8*x^3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x])*(16*x - 44*x^2 - 16*x^3 + (32*x + 12*x^2)*Log[x])
+ E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*(4 + 16*x^2 - 44*x^3 - 16*x^4 + (32*x^2 + 12*x^3)*Log[x]))/((5 + E^
(-8*x^3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2)*Log[5 + E^(-8*x
^3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2]*Log[Log[5 + E^(-8*x^
3 - 2*x^4 + 2*(4*x^2 + x^3)*Log[x]) + 2*E^(-4*x^3 - x^4 + (4*x^2 + x^3)*Log[x])*x + x^2]]),x]

[Out]

2*Log[Log[Log[5 + x^2 + E^(-8*x^3 - 2*x^4)*x^(2*x^2*(4 + x)) + 2*E^(-4*x^3 - x^4)*x^(1 + x^2*(4 + x))]]]

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(52\) vs. \(2(25)=50\).
time = 0.06, size = 53, normalized size = 2.04

method	result	size
risch	\(2 \ln \left (\ln \left (\ln \left (x^{2 x^{2} \left (4+x \right )} {\mathrm e}^{-2 x^{3} \left (4+x \right )}+2 x \,x^{x^{2} \left (4+x \right )} {\mathrm e}^{-x^{3} \left (4+x \right )}+x^{2}+5\right )\right )\right )\)	\(53\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((12*x^2+32*x)*ln(x)-16*x^3-44*x^2+16*x)*exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)^2+((12*x^3+32*x^2)*ln(x)-16*x^4
-44*x^3+16*x^2+4)*exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)+4*x)/(exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2
)*ln(x)-x^4-4*x^3)+x^2+5)/ln(exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)+x^2+5)/ln
(ln(exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*ln(x)-x^4-4*x^3)+x^2+5)),x,method=_RETURNVERBOSE)

[Out]

2*ln(ln(ln((x^(x^2*(4+x)))^2*exp(-2*x^3*(4+x))+2*x*x^(x^2*(4+x))*exp(-x^3*(4+x))+x^2+5)))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (26) = 52\).
time = 0.46, size = 77, normalized size = 2.96 \begin {gather*} 2 \, \log \left (\log \left (-2 \, x^{4} - 8 \, x^{3} + \log \left ({\left (x^{2} + 5\right )} e^{\left (2 \, x^{4} + 8 \, x^{3}\right )} + 2 \, x e^{\left (x^{4} + x^{3} \log \left (x\right ) + 4 \, x^{3} + 4 \, x^{2} \log \left (x\right )\right )} + e^{\left (2 \, x^{3} \log \left (x\right ) + 8 \, x^{2} \log \left (x\right )\right )}\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^2+32*x)*log(x)-16*x^3-44*x^2+16*x)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+((12*x^3+32*x^2)*log(
x)-16*x^4-44*x^3+16*x^2+4)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+4*x)/(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp
((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)/log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4
*x^3)+x^2+5)/log(log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)),x, algo
rithm="maxima")

[Out]

2*log(log(-2*x^4 - 8*x^3 + log((x^2 + 5)*e^(2*x^4 + 8*x^3) + 2*x*e^(x^4 + x^3*log(x) + 4*x^3 + 4*x^2*log(x)) +
e^(2*x^3*log(x) + 8*x^2*log(x)))))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (26) = 52\).
time = 0.37, size = 62, normalized size = 2.38 \begin {gather*} 2 \, \log \left (\log \left (\log \left (x^{2} + 2 \, x e^{\left (-x^{4} - 4 \, x^{3} + {\left (x^{3} + 4 \, x^{2}\right )} \log \left (x\right )\right )} + e^{\left (-2 \, x^{4} - 8 \, x^{3} + 2 \, {\left (x^{3} + 4 \, x^{2}\right )} \log \left (x\right )\right )} + 5\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^2+32*x)*log(x)-16*x^3-44*x^2+16*x)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+((12*x^3+32*x^2)*log(
x)-16*x^4-44*x^3+16*x^2+4)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+4*x)/(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp
((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)/log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4
*x^3)+x^2+5)/log(log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)),x, algo
rithm="fricas")

[Out]

2*log(log(log(x^2 + 2*x*e^(-x^4 - 4*x^3 + (x^3 + 4*x^2)*log(x)) + e^(-2*x^4 - 8*x^3 + 2*(x^3 + 4*x^2)*log(x))
+ 5)))

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x**2+32*x)*ln(x)-16*x**3-44*x**2+16*x)*exp((x**3+4*x**2)*ln(x)-x**4-4*x**3)**2+((12*x**3+32*x*
*2)*ln(x)-16*x**4-44*x**3+16*x**2+4)*exp((x**3+4*x**2)*ln(x)-x**4-4*x**3)+4*x)/(exp((x**3+4*x**2)*ln(x)-x**4-4
*x**3)**2+2*x*exp((x**3+4*x**2)*ln(x)-x**4-4*x**3)+x**2+5)/ln(exp((x**3+4*x**2)*ln(x)-x**4-4*x**3)**2+2*x*exp(
(x**3+4*x**2)*ln(x)-x**4-4*x**3)+x**2+5)/ln(ln(exp((x**3+4*x**2)*ln(x)-x**4-4*x**3)**2+2*x*exp((x**3+4*x**2)*l
n(x)-x**4-4*x**3)+x**2+5)),x)

[Out]

Timed out

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (26) = 52\).
time = 2.43, size = 64, normalized size = 2.46 \begin {gather*} 2 \, \log \left (\log \left (\log \left (x^{2} + 2 \, x e^{\left (-x^{4} + x^{3} \log \left (x\right ) - 4 \, x^{3} + 4 \, x^{2} \log \left (x\right )\right )} + e^{\left (-2 \, x^{4} + 2 \, x^{3} \log \left (x\right ) - 8 \, x^{3} + 8 \, x^{2} \log \left (x\right )\right )} + 5\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((12*x^2+32*x)*log(x)-16*x^3-44*x^2+16*x)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+((12*x^3+32*x^2)*log(
x)-16*x^4-44*x^3+16*x^2+4)*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+4*x)/(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp
((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)/log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4
*x^3)+x^2+5)/log(log(exp((x^3+4*x^2)*log(x)-x^4-4*x^3)^2+2*x*exp((x^3+4*x^2)*log(x)-x^4-4*x^3)+x^2+5)),x, algo
rithm="giac")

[Out]

2*log(log(log(x^2 + 2*x*e^(-x^4 + x^3*log(x) - 4*x^3 + 4*x^2*log(x)) + e^(-2*x^4 + 2*x^3*log(x) - 8*x^3 + 8*x^
2*log(x)) + 5)))

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Mupad [B]
time = 8.27, size = 62, normalized size = 2.38 \begin {gather*} 2\,\ln \left (\ln \left (\ln \left (x^2+x^{2\,x^3+8\,x^2}\,{\mathrm {e}}^{-2\,x^4}\,{\mathrm {e}}^{-8\,x^3}+2\,x^{x^3+4\,x^2+1}\,{\mathrm {e}}^{-x^4}\,{\mathrm {e}}^{-4\,x^3}+5\right )\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x + exp(log(x)*(4*x^2 + x^3) - 4*x^3 - x^4)*(log(x)*(32*x^2 + 12*x^3) + 16*x^2 - 44*x^3 - 16*x^4 + 4) +
exp(2*log(x)*(4*x^2 + x^3) - 8*x^3 - 2*x^4)*(16*x + log(x)*(32*x + 12*x^2) - 44*x^2 - 16*x^3))/(log(exp(2*log
(x)*(4*x^2 + x^3) - 8*x^3 - 2*x^4) + 2*x*exp(log(x)*(4*x^2 + x^3) - 4*x^3 - x^4) + x^2 + 5)*log(log(exp(2*log(
x)*(4*x^2 + x^3) - 8*x^3 - 2*x^4) + 2*x*exp(log(x)*(4*x^2 + x^3) - 4*x^3 - x^4) + x^2 + 5))*(exp(2*log(x)*(4*x
^2 + x^3) - 8*x^3 - 2*x^4) + 2*x*exp(log(x)*(4*x^2 + x^3) - 4*x^3 - x^4) + x^2 + 5)),x)

[Out]

2*log(log(log(x^2 + x^(8*x^2 + 2*x^3)*exp(-2*x^4)*exp(-8*x^3) + 2*x^(4*x^2 + x^3 + 1)*exp(-x^4)*exp(-4*x^3) +
5)))

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