3.86.77 \(\int \frac {e^{\frac {4 x+x^3-x^4+x^2 \log (4 e^x+e^x \log (x^2))}{-4+x^3}} (-128-16 x-128 x^2+64 x^3+4 x^4+8 x^5-8 x^6+(-32-32 x^2+16 x^3+2 x^5-2 x^6) \log (x^2)+(-64 x-8 x^4+(-16 x-2 x^4) \log (x^2)) \log (4 e^x+e^x \log (x^2)))}{64-32 x^3+4 x^6+(16-8 x^3+x^6) \log (x^2)} \, dx\)

Optimal. Leaf size=31 \[ 2 e^{-x+\frac {x+\log \left (e^x \left (4+\log \left (x^2\right )\right )\right )}{-\frac {4}{x^2}+x}} \]

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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[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*(-128 - 16*x - 128*x^2 + 64*x^3 + 4*x^4
+ 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Log[x^2]
)*Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6)*Log[x^2]),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 0.37, size = 64, normalized size = 2.06 \begin {gather*} 2 e^{\frac {x \left (4+x^2-x^3-x \log \left (4+\log \left (x^2\right )\right )+x \log \left (e^x \left (4+\log \left (x^2\right )\right )\right )\right )}{-4+x^3}} \left (4+\log \left (x^2\right )\right )^{\frac {x^2}{-4+x^3}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((4*x + x^3 - x^4 + x^2*Log[4*E^x + E^x*Log[x^2]])/(-4 + x^3))*(-128 - 16*x - 128*x^2 + 64*x^3 +
4*x^4 + 8*x^5 - 8*x^6 + (-32 - 32*x^2 + 16*x^3 + 2*x^5 - 2*x^6)*Log[x^2] + (-64*x - 8*x^4 + (-16*x - 2*x^4)*Lo
g[x^2])*Log[4*E^x + E^x*Log[x^2]]))/(64 - 32*x^3 + 4*x^6 + (16 - 8*x^3 + x^6)*Log[x^2]),x]

[Out]

2*E^((x*(4 + x^2 - x^3 - x*Log[4 + Log[x^2]] + x*Log[E^x*(4 + Log[x^2])]))/(-4 + x^3))*(4 + Log[x^2])^(x^2/(-4
+ x^3))

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fricas [A]  time = 0.63, size = 42, normalized size = 1.35 \begin {gather*} 2 \, e^{\left (-\frac {x^{4} - x^{3} - x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right ) - 4 \, x}{x^{3} - 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.93, size = 61, normalized size = 1.97 \begin {gather*} 2 \, e^{\left (-\frac {x^{4}}{x^{3} - 4} + \frac {x^{3}}{x^{3} - 4} + \frac {x^{2} \log \left (e^{x} \log \left (x^{2}\right ) + 4 \, e^{x}\right )}{x^{3} - 4} + \frac {4 \, x}{x^{3} - 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="giac")

[Out]

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

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maple [C]  time = 0.53, size = 545, normalized size = 17.58

method	result	size
risch	\(2 \,{\mathrm e}^{-\frac {x \left (-i x \pi \mathrm {csgn}\left (i {\mathrm e}^{x} \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )^{3}-i x \pi \mathrm {csgn}\left (i {\mathrm e}^{x} \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{x}\right )-i x \pi \mathrm {csgn}\left (i {\mathrm e}^{x} \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2} \mathrm {csgn}\left (i \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )+i x \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x} \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )+2 i x \pi \mathrm {csgn}\left (i {\mathrm e}^{x} \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )\right )^{2}-2 i \pi x +2 x^{3}+2 x \ln \relax (2)-2 x \ln \left ({\mathrm e}^{x}\right )-2 x \ln \left (8 i+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \ln \relax (x )+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}\right )-2 x^{2}-8\right )}{2 \left (x^{3}-4\right )}}\)	\(545\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^4-16*x)*ln(x^2)-8*x^4-64*x)*ln(exp(x)*ln(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*ln(x^2)-8*
x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*ln(exp(x)*ln(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4))/((x^6-8*x^
3+16)*ln(x^2)+4*x^6-32*x^3+64),x,method=_RETURNVERBOSE)

[Out]

2*exp(-1/2*x*(-I*x*Pi*csgn(I*exp(x)*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+4*I*ln(x)+Pi*
csgn(I*x^2)^3))^3-I*x*Pi*csgn(I*exp(x)*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+4*I*ln(x)+
Pi*csgn(I*x^2)^3))^2*csgn(I*exp(x))-I*x*Pi*csgn(I*exp(x)*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I
*x^2)^2+4*I*ln(x)+Pi*csgn(I*x^2)^3))^2*csgn(I*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+4*I
*ln(x)+Pi*csgn(I*x^2)^3))+I*x*Pi*csgn(I*exp(x)*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+4*
I*ln(x)+Pi*csgn(I*x^2)^3))*csgn(I*exp(x))*csgn(I*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+
4*I*ln(x)+Pi*csgn(I*x^2)^3))+2*I*x*Pi*csgn(I*exp(x)*(8*I+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)
^2+4*I*ln(x)+Pi*csgn(I*x^2)^3))^2-2*I*Pi*x+2*x^3+2*x*ln(2)-2*x*ln(exp(x))-2*x*ln(8*I+Pi*csgn(I*x)^2*csgn(I*x^2
)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+4*I*ln(x)+Pi*csgn(I*x^2)^3)-2*x^2-8)/(x^3-4))

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maxima [A]  time = 0.62, size = 46, normalized size = 1.48 \begin {gather*} 2 \, e^{\left (\frac {x^{2} \log \relax (2)}{x^{3} - 4} + \frac {x^{2} \log \left (\log \relax (x) + 2\right )}{x^{3} - 4} - x + \frac {8}{x^{3} - 4} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^4-16*x)*log(x^2)-8*x^4-64*x)*log(exp(x)*log(x^2)+4*exp(x))+(-2*x^6+2*x^5+16*x^3-32*x^2-32)*l
og(x^2)-8*x^6+8*x^5+4*x^4+64*x^3-128*x^2-16*x-128)*exp((x^2*log(exp(x)*log(x^2)+4*exp(x))-x^4+x^3+4*x)/(x^3-4)
)/((x^6-8*x^3+16)*log(x^2)+4*x^6-32*x^3+64),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 5.67, size = 62, normalized size = 2.00 \begin {gather*} 2\,{\mathrm {e}}^{\frac {x^3}{x^3-4}}\,{\mathrm {e}}^{-\frac {x^4}{x^3-4}}\,{\mathrm {e}}^{\frac {4\,x}{x^3-4}}\,{\left (4\,{\mathrm {e}}^x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}^{\frac {x^2}{x^3-4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((4*x + x^2*log(4*exp(x) + log(x^2)*exp(x)) + x^3 - x^4)/(x^3 - 4))*(16*x + log(4*exp(x) + log(x^2)*e
xp(x))*(64*x + log(x^2)*(16*x + 2*x^4) + 8*x^4) + 128*x^2 - 64*x^3 - 4*x^4 - 8*x^5 + 8*x^6 + log(x^2)*(32*x^2
- 16*x^3 - 2*x^5 + 2*x^6 + 32) + 128))/(log(x^2)*(x^6 - 8*x^3 + 16) - 32*x^3 + 4*x^6 + 64),x)

[Out]

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

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sympy [F(-1)]  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((((-2*x**4-16*x)*ln(x**2)-8*x**4-64*x)*ln(exp(x)*ln(x**2)+4*exp(x))+(-2*x**6+2*x**5+16*x**3-32*x**2-
32)*ln(x**2)-8*x**6+8*x**5+4*x**4+64*x**3-128*x**2-16*x-128)*exp((x**2*ln(exp(x)*ln(x**2)+4*exp(x))-x**4+x**3+
4*x)/(x**3-4))/((x**6-8*x**3+16)*ln(x**2)+4*x**6-32*x**3+64),x)

[Out]

Timed out

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