3.9.38 \(\int \frac {e^{\frac {-16+32 x-2 x^4+(32-64 x) \log (x^2)+(-24+48 x) \log ^2(x^2)+(8-16 x) \log ^3(x^2)+(-1+2 x) \log ^4(x^2)}{32-64 \log (x^2)+48 \log ^2(x^2)-16 \log ^3(x^2)+2 \log ^4(x^2)}} (-32+16 x^3+(80-4 x^3) \log (x^2)-80 \log ^2(x^2)+40 \log ^3(x^2)-10 \log ^4(x^2)+\log ^5(x^2))}{-32+80 \log (x^2)-80 \log ^2(x^2)+40 \log ^3(x^2)-10 \log ^4(x^2)+\log ^5(x^2)} \, dx\)

Optimal. Leaf size=20 \[ e^{-\frac {1}{2}+x-\frac {x^4}{\left (-2+\log \left (x^2\right )\right )^4}} \]

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Rubi [F]  time = 15.18, 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 {\exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{32-64 \log \left (x^2\right )+48 \log ^2\left (x^2\right )-16 \log ^3\left (x^2\right )+2 \log ^4\left (x^2\right )}\right ) \left (-32+16 x^3+\left (80-4 x^3\right ) \log \left (x^2\right )-80 \log ^2\left (x^2\right )+40 \log ^3\left (x^2\right )-10 \log ^4\left (x^2\right )+\log ^5\left (x^2\right )\right )}{-32+80 \log \left (x^2\right )-80 \log ^2\left (x^2\right )+40 \log ^3\left (x^2\right )-10 \log ^4\left (x^2\right )+\log ^5\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-16 + 32*x - 2*x^4 + (32 - 64*x)*Log[x^2] + (-24 + 48*x)*Log[x^2]^2 + (8 - 16*x)*Log[x^2]^3 + (-1 + 2
*x)*Log[x^2]^4)/(32 - 64*Log[x^2] + 48*Log[x^2]^2 - 16*Log[x^2]^3 + 2*Log[x^2]^4))*(-32 + 16*x^3 + (80 - 4*x^3
)*Log[x^2] - 80*Log[x^2]^2 + 40*Log[x^2]^3 - 10*Log[x^2]^4 + Log[x^2]^5))/(-32 + 80*Log[x^2] - 80*Log[x^2]^2 +
40*Log[x^2]^3 - 10*Log[x^2]^4 + Log[x^2]^5),x]

[Out]

Defer[Int][E^((-16 + 32*x - 2*x^4 + (32 - 64*x)*Log[x^2] + (-24 + 48*x)*Log[x^2]^2 + (8 - 16*x)*Log[x^2]^3 + (
-1 + 2*x)*Log[x^2]^4)/(2*(-2 + Log[x^2])^4)), x] + 8*Defer[Int][(E^((-16 + 32*x - 2*x^4 + (32 - 64*x)*Log[x^2]
+ (-24 + 48*x)*Log[x^2]^2 + (8 - 16*x)*Log[x^2]^3 + (-1 + 2*x)*Log[x^2]^4)/(2*(-2 + Log[x^2])^4))*x^3)/(-2 +
Log[x^2])^5, x] - 4*Defer[Int][(E^((-16 + 32*x - 2*x^4 + (32 - 64*x)*Log[x^2] + (-24 + 48*x)*Log[x^2]^2 + (8 -
16*x)*Log[x^2]^3 + (-1 + 2*x)*Log[x^2]^4)/(2*(-2 + Log[x^2])^4))*x^3)/(-2 + Log[x^2])^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) \left (32-16 x^3-\left (80-4 x^3\right ) \log \left (x^2\right )+80 \log ^2\left (x^2\right )-40 \log ^3\left (x^2\right )+10 \log ^4\left (x^2\right )-\log ^5\left (x^2\right )\right )}{\left (2-\log \left (x^2\right )\right )^5} \, dx\\ &=\int \left (\exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right )+\frac {8 \exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) x^3}{\left (-2+\log \left (x^2\right )\right )^5}-\frac {4 \exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) x^3}{\left (-2+\log \left (x^2\right )\right )^4}\right ) \, dx\\ &=-\left (4 \int \frac {\exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) x^3}{\left (-2+\log \left (x^2\right )\right )^4} \, dx\right )+8 \int \frac {\exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) x^3}{\left (-2+\log \left (x^2\right )\right )^5} \, dx+\int \exp \left (\frac {-16+32 x-2 x^4+(32-64 x) \log \left (x^2\right )+(-24+48 x) \log ^2\left (x^2\right )+(8-16 x) \log ^3\left (x^2\right )+(-1+2 x) \log ^4\left (x^2\right )}{2 \left (-2+\log \left (x^2\right )\right )^4}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.39, size = 61, normalized size = 3.05 \begin {gather*} e^{-\frac {1}{2}+x+\frac {-32+64 x-x^4}{\left (-2+\log \left (x^2\right )\right )^4}+\frac {16 (-1+2 x)}{\left (-2+\log \left (x^2\right )\right )^3}} \left (x^2\right )^{-\frac {16 (-1+2 x)}{\left (-2+\log \left (x^2\right )\right )^4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-16 + 32*x - 2*x^4 + (32 - 64*x)*Log[x^2] + (-24 + 48*x)*Log[x^2]^2 + (8 - 16*x)*Log[x^2]^3 + (
-1 + 2*x)*Log[x^2]^4)/(32 - 64*Log[x^2] + 48*Log[x^2]^2 - 16*Log[x^2]^3 + 2*Log[x^2]^4))*(-32 + 16*x^3 + (80 -
4*x^3)*Log[x^2] - 80*Log[x^2]^2 + 40*Log[x^2]^3 - 10*Log[x^2]^4 + Log[x^2]^5))/(-32 + 80*Log[x^2] - 80*Log[x^
2]^2 + 40*Log[x^2]^3 - 10*Log[x^2]^4 + Log[x^2]^5),x]

[Out]

E^(-1/2 + x + (-32 + 64*x - x^4)/(-2 + Log[x^2])^4 + (16*(-1 + 2*x))/(-2 + Log[x^2])^3)/(x^2)^((16*(-1 + 2*x))
/(-2 + Log[x^2])^4)

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fricas [B]  time = 0.69, size = 94, normalized size = 4.70 \begin {gather*} e^{\left (\frac {{\left (2 \, x - 1\right )} \log \left (x^{2}\right )^{4} - 2 \, x^{4} - 8 \, {\left (2 \, x - 1\right )} \log \left (x^{2}\right )^{3} + 24 \, {\left (2 \, x - 1\right )} \log \left (x^{2}\right )^{2} - 32 \, {\left (2 \, x - 1\right )} \log \left (x^{2}\right ) + 32 \, x - 16}{2 \, {\left (\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+(-4*x^3+80)*log(x^2)+16*x^3-32)*exp(((2*x-1)*l
og(x^2)^4+(-16*x+8)*log(x^2)^3+(48*x-24)*log(x^2)^2+(-64*x+32)*log(x^2)-2*x^4+32*x-16)/(2*log(x^2)^4-16*log(x^
2)^3+48*log(x^2)^2-64*log(x^2)+32))/(log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+80*log(x^2)-32),x, a
lgorithm="fricas")

[Out]

e^(1/2*((2*x - 1)*log(x^2)^4 - 2*x^4 - 8*(2*x - 1)*log(x^2)^3 + 24*(2*x - 1)*log(x^2)^2 - 32*(2*x - 1)*log(x^2
) + 32*x - 16)/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16))

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giac [B]  time = 5.78, size = 427, normalized size = 21.35 \begin {gather*} e^{\left (\frac {x \log \left (x^{2}\right )^{4}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {x^{4}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {8 \, x \log \left (x^{2}\right )^{3}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {\log \left (x^{2}\right )^{4}}{2 \, {\left (\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16\right )}} + \frac {24 \, x \log \left (x^{2}\right )^{2}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} + \frac {4 \, \log \left (x^{2}\right )^{3}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {32 \, x \log \left (x^{2}\right )}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {12 \, \log \left (x^{2}\right )^{2}}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} + \frac {16 \, x}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} + \frac {16 \, \log \left (x^{2}\right )}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16} - \frac {8}{\log \left (x^{2}\right )^{4} - 8 \, \log \left (x^{2}\right )^{3} + 24 \, \log \left (x^{2}\right )^{2} - 32 \, \log \left (x^{2}\right ) + 16}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+(-4*x^3+80)*log(x^2)+16*x^3-32)*exp(((2*x-1)*l
og(x^2)^4+(-16*x+8)*log(x^2)^3+(48*x-24)*log(x^2)^2+(-64*x+32)*log(x^2)-2*x^4+32*x-16)/(2*log(x^2)^4-16*log(x^
2)^3+48*log(x^2)^2-64*log(x^2)+32))/(log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+80*log(x^2)-32),x, a
lgorithm="giac")

[Out]

e^(x*log(x^2)^4/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16) - x^4/(log(x^2)^4 - 8*log(x^2)^
3 + 24*log(x^2)^2 - 32*log(x^2) + 16) - 8*x*log(x^2)^3/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2
) + 16) - 1/2*log(x^2)^4/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16) + 24*x*log(x^2)^2/(log
(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16) + 4*log(x^2)^3/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(
x^2)^2 - 32*log(x^2) + 16) - 32*x*log(x^2)/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16) - 12
*log(x^2)^2/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16) + 16*x/(log(x^2)^4 - 8*log(x^2)^3 +
24*log(x^2)^2 - 32*log(x^2) + 16) + 16*log(x^2)/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16
) - 8/(log(x^2)^4 - 8*log(x^2)^3 + 24*log(x^2)^2 - 32*log(x^2) + 16))

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maple [B]  time = 0.80, size = 86, normalized size = 4.30

method	result	size
risch	\({\mathrm e}^{\frac {2 x \ln \left (x^{2}\right )^{4}-\ln \left (x^{2}\right )^{4}-16 x \ln \left (x^{2}\right )^{3}-2 x^{4}+8 \ln \left (x^{2}\right )^{3}+48 x \ln \left (x^{2}\right )^{2}-24 \ln \left (x^{2}\right )^{2}-64 x \ln \left (x^{2}\right )+32 \ln \left (x^{2}\right )+32 x -16}{2 \left (-2+\ln \left (x^{2}\right )\right )^{4}}}\)	\(86\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((ln(x^2)^5-10*ln(x^2)^4+40*ln(x^2)^3-80*ln(x^2)^2+(-4*x^3+80)*ln(x^2)+16*x^3-32)*exp(((2*x-1)*ln(x^2)^4+(-
16*x+8)*ln(x^2)^3+(48*x-24)*ln(x^2)^2+(-64*x+32)*ln(x^2)-2*x^4+32*x-16)/(2*ln(x^2)^4-16*ln(x^2)^3+48*ln(x^2)^2
-64*ln(x^2)+32))/(ln(x^2)^5-10*ln(x^2)^4+40*ln(x^2)^3-80*ln(x^2)^2+80*ln(x^2)-32),x,method=_RETURNVERBOSE)

[Out]

exp(1/2*(2*x*ln(x^2)^4-ln(x^2)^4-16*x*ln(x^2)^3-2*x^4+8*ln(x^2)^3+48*x*ln(x^2)^2-24*ln(x^2)^2-64*x*ln(x^2)+32*
ln(x^2)+32*x-16)/(-2+ln(x^2))^4)

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maxima [B]  time = 1.27, size = 322, normalized size = 16.10 \begin {gather*} e^{\left (\frac {x \log \relax (x)^{4}}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} - \frac {x^{4}}{16 \, {\left (\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )}} - \frac {4 \, x \log \relax (x)^{3}}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} - \frac {\log \relax (x)^{4}}{2 \, {\left (\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )}} + \frac {6 \, x \log \relax (x)^{2}}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} + \frac {2 \, \log \relax (x)^{3}}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} - \frac {4 \, x \log \relax (x)}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} - \frac {3 \, \log \relax (x)^{2}}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} + \frac {x}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} + \frac {2 \, \log \relax (x)}{\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1} - \frac {1}{2 \, {\left (\log \relax (x)^{4} - 4 \, \log \relax (x)^{3} + 6 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+(-4*x^3+80)*log(x^2)+16*x^3-32)*exp(((2*x-1)*l
og(x^2)^4+(-16*x+8)*log(x^2)^3+(48*x-24)*log(x^2)^2+(-64*x+32)*log(x^2)-2*x^4+32*x-16)/(2*log(x^2)^4-16*log(x^
2)^3+48*log(x^2)^2-64*log(x^2)+32))/(log(x^2)^5-10*log(x^2)^4+40*log(x^2)^3-80*log(x^2)^2+80*log(x^2)-32),x, a
lgorithm="maxima")

[Out]

e^(x*log(x)^4/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) - 1/16*x^4/(log(x)^4 - 4*log(x)^3 + 6*log(x)
^2 - 4*log(x) + 1) - 4*x*log(x)^3/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) - 1/2*log(x)^4/(log(x)^4
- 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) + 6*x*log(x)^2/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1)
+ 2*log(x)^3/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) - 4*x*log(x)/(log(x)^4 - 4*log(x)^3 + 6*log(x
)^2 - 4*log(x) + 1) - 3*log(x)^2/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) + x/(log(x)^4 - 4*log(x)^
3 + 6*log(x)^2 - 4*log(x) + 1) + 2*log(x)/(log(x)^4 - 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1) - 1/2/(log(x)^4
- 4*log(x)^3 + 6*log(x)^2 - 4*log(x) + 1))

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mupad [B]  time = 0.99, size = 419, normalized size = 20.95 \begin {gather*} {\mathrm {e}}^{-\frac {2\,x^4}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{-\frac {16}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{\frac {2\,x\,{\ln \left (x^2\right )}^4}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{-\frac {16\,x\,{\ln \left (x^2\right )}^3}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{\frac {48\,x\,{\ln \left (x^2\right )}^2}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{\frac {32\,x}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{-\frac {{\ln \left (x^2\right )}^4}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{\frac {8\,{\ln \left (x^2\right )}^3}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\mathrm {e}}^{-\frac {24\,{\ln \left (x^2\right )}^2}{2\,{\ln \left (x^2\right )}^4-16\,{\ln \left (x^2\right )}^3+48\,{\ln \left (x^2\right )}^2-64\,\ln \left (x^2\right )+32}}\,{\left (\frac {1}{x^{32}}\right )}^{\frac {2\,x-1}{{\ln \left (x^2\right )}^4-8\,{\ln \left (x^2\right )}^3+24\,{\ln \left (x^2\right )}^2-32\,\ln \left (x^2\right )+16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(log(x^2)^3*(16*x - 8) - log(x^2)^4*(2*x - 1) - 32*x - log(x^2)^2*(48*x - 24) + 2*x^4 + log(x^2)*(6
4*x - 32) + 16)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*(log(x^2)*(4*x^3 - 80) + 80
*log(x^2)^2 - 40*log(x^2)^3 + 10*log(x^2)^4 - log(x^2)^5 - 16*x^3 + 32))/(80*log(x^2) - 80*log(x^2)^2 + 40*log
(x^2)^3 - 10*log(x^2)^4 + log(x^2)^5 - 32),x)

[Out]

exp(-(2*x^4)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*exp(-16/(48*log(x^2)^2 - 64*lo
g(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*exp((2*x*log(x^2)^4)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3
+ 2*log(x^2)^4 + 32))*exp(-(16*x*log(x^2)^3)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32
))*exp((48*x*log(x^2)^2)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*exp((32*x)/(48*log
(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*exp(-log(x^2)^4/(48*log(x^2)^2 - 64*log(x^2) - 16*
log(x^2)^3 + 2*log(x^2)^4 + 32))*exp((8*log(x^2)^3)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^
4 + 32))*exp(-(24*log(x^2)^2)/(48*log(x^2)^2 - 64*log(x^2) - 16*log(x^2)^3 + 2*log(x^2)^4 + 32))*(1/x^32)^((2*
x - 1)/(24*log(x^2)^2 - 32*log(x^2) - 8*log(x^2)^3 + log(x^2)^4 + 16))

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sympy [B]  time = 0.87, size = 90, normalized size = 4.50 \begin {gather*} e^{\frac {- 2 x^{4} + 32 x + \left (8 - 16 x\right ) \log {\left (x^{2} \right )}^{3} + \left (32 - 64 x\right ) \log {\left (x^{2} \right )} + \left (2 x - 1\right ) \log {\left (x^{2} \right )}^{4} + \left (48 x - 24\right ) \log {\left (x^{2} \right )}^{2} - 16}{2 \log {\left (x^{2} \right )}^{4} - 16 \log {\left (x^{2} \right )}^{3} + 48 \log {\left (x^{2} \right )}^{2} - 64 \log {\left (x^{2} \right )} + 32}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((ln(x**2)**5-10*ln(x**2)**4+40*ln(x**2)**3-80*ln(x**2)**2+(-4*x**3+80)*ln(x**2)+16*x**3-32)*exp(((2*
x-1)*ln(x**2)**4+(-16*x+8)*ln(x**2)**3+(48*x-24)*ln(x**2)**2+(-64*x+32)*ln(x**2)-2*x**4+32*x-16)/(2*ln(x**2)**
4-16*ln(x**2)**3+48*ln(x**2)**2-64*ln(x**2)+32))/(ln(x**2)**5-10*ln(x**2)**4+40*ln(x**2)**3-80*ln(x**2)**2+80*
ln(x**2)-32),x)

[Out]

exp((-2*x**4 + 32*x + (8 - 16*x)*log(x**2)**3 + (32 - 64*x)*log(x**2) + (2*x - 1)*log(x**2)**4 + (48*x - 24)*l
og(x**2)**2 - 16)/(2*log(x**2)**4 - 16*log(x**2)**3 + 48*log(x**2)**2 - 64*log(x**2) + 32))

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