Optimal. Leaf size=28 \[ 1-e^{\frac {1}{\left (2-e^{2-16 \left (x^2-\log (4)\right )^2}\right )^2}} \]
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Rubi [F] time = 27.06, 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 (2+\frac {1}{4+e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)}-4 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)}}-16 x^4+32 x^2 \log (4)-16 \log ^2(4)\right ) \left (-128 x^4+128 x^2 \log (4)\right )}{-8 x+e^{6-48 x^4+96 x^2 \log (4)-48 \log ^2(4)} x-6 e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)} x+12 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)} x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (2+\frac {1}{4+e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)}-4 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)}}-16 x^4+32 x^2 \log (4)-16 \log ^2(4)\right ) x^2 \left (-128 x^2+128 \log (4)\right )}{-8 x+e^{6-48 x^4+96 x^2 \log (4)-48 \log ^2(4)} x-6 e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)} x+12 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)} x} \, dx\\ &=\int \frac {2^{7+64 x^2} \exp \left (\frac {e^{32 \left (x^4+\log ^2(4)\right )}}{\left (2^{64 x^2} e^2-2 e^{16 \left (x^4+\log ^2(4)\right )}\right )^2}+32 x^4+2 \left (1+16 \log ^2(4)\right )\right ) x \left (-x^2+\log (4)\right )}{\left (2^{64 x^2} e^2-2 e^{16 \left (x^4+\log ^2(4)\right )}\right )^3} \, dx\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {2^{7+64 x} \exp \left (\frac {e^{32 \left (x^2+\log ^2(4)\right )}}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^2}+32 x^2+2 \left (1+16 \log ^2(4)\right )\right ) (-x+\log (4))}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^3} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {2^{7+64 x} \exp \left (\frac {e^{32 \left (x^2+\log ^2(4)\right )}}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^2}+32 x^2+2 \left (1+16 \log ^2(4)\right )\right ) x}{\left (-2^{64 x} e^2+2 e^{16 x^2+16 \log ^2(4)}\right )^3}-\frac {2^{7+64 x} \exp \left (\frac {e^{32 \left (x^2+\log ^2(4)\right )}}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^2}+32 x^2+2 \left (1+16 \log ^2(4)\right )\right ) \log (4)}{\left (-2^{64 x} e^2+2 e^{16 x^2+16 \log ^2(4)}\right )^3}\right ) \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {2^{7+64 x} \exp \left (\frac {e^{32 \left (x^2+\log ^2(4)\right )}}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^2}+32 x^2+2 \left (1+16 \log ^2(4)\right )\right ) x}{\left (-2^{64 x} e^2+2 e^{16 x^2+16 \log ^2(4)}\right )^3} \, dx,x,x^2\right )-\frac {1}{2} \log (4) \operatorname {Subst}\left (\int \frac {2^{7+64 x} \exp \left (\frac {e^{32 \left (x^2+\log ^2(4)\right )}}{\left (2^{64 x} e^2-2 e^{16 \left (x^2+\log ^2(4)\right )}\right )^2}+32 x^2+2 \left (1+16 \log ^2(4)\right )\right )}{\left (-2^{64 x} e^2+2 e^{16 x^2+16 \log ^2(4)}\right )^3} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 9.80, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{2+\frac {1}{4+e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)}-4 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)}}-16 x^4+32 x^2 \log (4)-16 \log ^2(4)} \left (-128 x^4+128 x^2 \log (4)\right )}{-8 x+e^{6-48 x^4+96 x^2 \log (4)-48 \log ^2(4)} x-6 e^{4-32 x^4+64 x^2 \log (4)-32 \log ^2(4)} x+12 e^{2-16 x^4+32 x^2 \log (4)-16 \log ^2(4)} x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.61, size = 180, normalized size = 6.43 \begin {gather*} -e^{\left (16 \, x^{4} - 64 \, x^{2} \log \relax (2) + 64 \, \log \relax (2)^{2} + \frac {64 \, x^{4} - 256 \, x^{2} \log \relax (2) - 8 \, {\left (8 \, x^{4} - 32 \, x^{2} \log \relax (2) + 32 \, \log \relax (2)^{2} - 1\right )} e^{\left (-16 \, x^{4} + 64 \, x^{2} \log \relax (2) - 64 \, \log \relax (2)^{2} + 2\right )} + 2 \, {\left (8 \, x^{4} - 32 \, x^{2} \log \relax (2) + 32 \, \log \relax (2)^{2} - 1\right )} e^{\left (-32 \, x^{4} + 128 \, x^{2} \log \relax (2) - 128 \, \log \relax (2)^{2} + 4\right )} + 256 \, \log \relax (2)^{2} - 9}{4 \, e^{\left (-16 \, x^{4} + 64 \, x^{2} \log \relax (2) - 64 \, \log \relax (2)^{2} + 2\right )} - e^{\left (-32 \, x^{4} + 128 \, x^{2} \log \relax (2) - 128 \, \log \relax (2)^{2} + 4\right )} - 4} - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 56, normalized size = 2.00
method | result | size |
risch | \(-{\mathrm e}^{-\frac {1}{-{\mathrm e}^{-32 x^{4}+128 x^{2} \ln \relax (2)-128 \ln \relax (2)^{2}+4}+4 \,{\mathrm e}^{-16 x^{4}+64 x^{2} \ln \relax (2)-64 \ln \relax (2)^{2}+2}-4}}\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.56, size = 68, normalized size = 2.43 \begin {gather*} -e^{\left (\frac {e^{\left (32 \, x^{4} + 128 \, \log \relax (2)^{2}\right )}}{4 \, e^{\left (32 \, x^{4} + 128 \, \log \relax (2)^{2}\right )} - 4 \, e^{\left (16 \, x^{4} + 64 \, x^{2} \log \relax (2) + 64 \, \log \relax (2)^{2} + 2\right )} + e^{\left (128 \, x^{2} \log \relax (2) + 4\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.00, size = 54, normalized size = 1.93 \begin {gather*} -{\mathrm {e}}^{\frac {1}{2^{128\,x^2}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-128\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{-32\,x^4}-4\,2^{64\,x^2}\,{\mathrm {e}}^2\,{\mathrm {e}}^{-64\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{-16\,x^4}+4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.58, size = 54, normalized size = 1.93 \begin {gather*} - e^{\frac {1}{e^{- 32 x^{4} + 128 x^{2} \log {\relax (2 )} - 128 \log {\relax (2 )}^{2} + 4} - 4 e^{- 16 x^{4} + 64 x^{2} \log {\relax (2 )} - 64 \log {\relax (2 )}^{2} + 2} + 4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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