Optimal. Leaf size=20 \[ \frac {81}{e^3 x^4 \log ^4\left (\log \left (\log \left (\frac {43}{2}+x^2\right )\right )\right )} \]
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Rubi [A]
time = 0.41, antiderivative size = 24, normalized size of antiderivative = 1.20, number of steps
used = 3, number of rules used = 3, integrand size = 115, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12, 1607,
6819} \begin {gather*} \frac {81}{e^3 x^4 \log ^4\left (\log \left (\log \left (\frac {1}{2} \left (2 x^2+43\right )\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1607
Rule 6819
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-1296 x^2+\left (-13932-648 x^2\right ) \log \left (\frac {1}{2} \left (43+2 x^2\right )\right ) \log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right ) \log \left (\log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right )\right )}{\left (43 x^5+2 x^7\right ) \log \left (\frac {1}{2} \left (43+2 x^2\right )\right ) \log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right ) \log ^5\left (\log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right )\right )} \, dx}{e^3}\\ &=\frac {\int \frac {-1296 x^2+\left (-13932-648 x^2\right ) \log \left (\frac {1}{2} \left (43+2 x^2\right )\right ) \log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right ) \log \left (\log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right )\right )}{x^5 \left (43+2 x^2\right ) \log \left (\frac {1}{2} \left (43+2 x^2\right )\right ) \log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right ) \log ^5\left (\log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right )\right )} \, dx}{e^3}\\ &=\frac {81}{e^3 x^4 \log ^4\left (\log \left (\log \left (\frac {1}{2} \left (43+2 x^2\right )\right )\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 20, normalized size = 1.00 \begin {gather*} \frac {81}{e^3 x^4 \log ^4\left (\log \left (\log \left (\frac {43}{2}+x^2\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 3.92, size = 18, normalized size = 0.90
method | result | size |
risch | \(\frac {81 \,{\mathrm e}^{-3}}{\ln \left (\ln \left (\ln \left (x^{2}+\frac {43}{2}\right )\right )\right )^{4} x^{4}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.57, size = 24, normalized size = 1.20 \begin {gather*} \frac {81 \, e^{\left (-3\right )}}{x^{4} \log \left (\log \left (-\log \left (2\right ) + \log \left (2 \, x^{2} + 43\right )\right )\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 17, normalized size = 0.85 \begin {gather*} \frac {81 \, e^{\left (-3\right )}}{x^{4} \log \left (\log \left (\log \left (x^{2} + \frac {43}{2}\right )\right )\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 20, normalized size = 1.00 \begin {gather*} \frac {81}{x^{4} e^{3} \log {\left (\log {\left (\log {\left (x^{2} + \frac {43}{2} \right )} \right )} \right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (17) = 34\).
time = 0.44, size = 58, normalized size = 2.90 \begin {gather*} \frac {324 \, e^{\left (-3\right )}}{{\left (2 \, x^{2} + 43\right )}^{2} \log \left (\log \left (\log \left (x^{2} + \frac {43}{2}\right )\right )\right )^{4} - 86 \, {\left (2 \, x^{2} + 43\right )} \log \left (\log \left (\log \left (x^{2} + \frac {43}{2}\right )\right )\right )^{4} + 1849 \, \log \left (\log \left (\log \left (x^{2} + \frac {43}{2}\right )\right )\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.89, size = 17, normalized size = 0.85 \begin {gather*} \frac {81\,{\mathrm {e}}^{-3}}{x^4\,{\ln \left (\ln \left (\ln \left (x^2+\frac {43}{2}\right )\right )\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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