Optimal. Leaf size=26 \[ -2-e^{3 \log ^2\left (\log ^2(2 x)\right )}+\left (-2+4 x^2\right )^2 \]
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Rubi [A]
time = 0.29, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 7, number of rules used = 5, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.102, Rules used = {6874, 14, 2308,
2235, 2240} \begin {gather*} 16 x^4-16 x^2-e^{3 \log ^2\left (\log ^2(2 x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2235
Rule 2240
Rule 2308
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (32 x \left (-1+2 x^2\right )-\frac {12 e^{3 \log ^2\left (\log ^2(2 x)\right )} \log \left (\log ^2(2 x)\right )}{x \log (2 x)}\right ) \, dx\\ &=-\left (12 \int \frac {e^{3 \log ^2\left (\log ^2(2 x)\right )} \log \left (\log ^2(2 x)\right )}{x \log (2 x)} \, dx\right )+32 \int x \left (-1+2 x^2\right ) \, dx\\ &=-\left (12 \text {Subst}\left (\int \frac {e^{3 \log ^2\left (x^2\right )} \log \left (x^2\right )}{x} \, dx,x,\log (2 x)\right )\right )+32 \int \left (-x+2 x^3\right ) \, dx\\ &=-16 x^2+16 x^4-6 \text {Subst}\left (\int e^{3 x^2} x \, dx,x,\log \left (\log ^2(2 x)\right )\right )\\ &=-e^{3 \log ^2\left (\log ^2(2 x)\right )}-16 x^2+16 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 26, normalized size = 1.00 \begin {gather*} -e^{3 \log ^2\left (\log ^2(2 x)\right )}-16 x^2+16 x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.57, size = 27, normalized size = 1.04
method | result | size |
default | \(4 \left (2 x^{2}-1\right )^{2}-{\mathrm e}^{3 \ln \left (\ln \left (2 x \right )^{2}\right )^{2}}\) | \(27\) |
risch | \(16 x^{4}-16 x^{2}+4-{\mathrm e}^{\frac {3 \left (i \pi \mathrm {csgn}\left (i \ln \left (2 x \right )^{2}\right )^{3}-2 i \pi \mathrm {csgn}\left (i \ln \left (2 x \right )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \left (2 x \right )\right )+i \pi \,\mathrm {csgn}\left (i \ln \left (2 x \right )^{2}\right ) \mathrm {csgn}\left (i \ln \left (2 x \right )\right )^{2}-4 \ln \left (\ln \left (2 x \right )\right )\right )^{2}}{4}}\) | \(92\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 25, normalized size = 0.96 \begin {gather*} 16 \, x^{4} - 16 \, x^{2} - e^{\left (3 \, \log \left (\log \left (2 \, x\right )^{2}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 25, normalized size = 0.96 \begin {gather*} 16 \, x^{4} - 16 \, x^{2} - e^{\left (3 \, \log \left (\log \left (2 \, x\right )^{2}\right )^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 22, normalized size = 0.85 \begin {gather*} 16 x^{4} - 16 x^{2} - e^{3 \log {\left (\log {\left (2 x \right )}^{2} \right )}^{2}} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.18, size = 34, normalized size = 1.31 \begin {gather*} 16\,x^4-16\,x^2-{\mathrm {e}}^{3\,{\ln \left ({\ln \left (x\right )}^2+2\,\ln \left (2\right )\,\ln \left (x\right )+{\ln \left (2\right )}^2\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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