Optimal. Leaf size=20 \[ \frac {1}{9} 4^{2 x^3} 5^{2-2 x^3} \]
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Rubi [C] Result contains higher order function than in optimal. Order 9 vs. order 3 in
optimal.
time = 40.37, antiderivative size = 67, normalized size of antiderivative = 3.35, number of steps
used = 986, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 2325,
2240} \begin {gather*} \frac {25 \log (2) \gcd \left (1,\frac {\log (5)}{\log (2)}\right ) \exp \left (-\frac {2 x^3 \log \left (\frac {5}{4}\right ) \log \left (2^{\gcd \left (1,\frac {\log (5)}{\log (2)}\right )}\right )}{\log (2) \gcd \left (1,\frac {\log (5)}{\log (2)}\right )}\right )}{9 \log \left (2^{\gcd \left (1,\frac {\log (5)}{\log (2)}\right )}\right )} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 12
Rule 2240
Rule 2325
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{3} \log \left (\frac {5}{4}\right ) \int 2^{1+4 x^3} 5^{2-2 x^3} x^2 \, dx\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 28, normalized size = 1.40 \begin {gather*} \frac {16^{x^3} 25^{1-x^3} \log \left (\frac {5}{4}\right )}{3 \log \left (\frac {125}{64}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.39, size = 12, normalized size = 0.60
method | result | size |
gosper | \(\frac {25 \,{\mathrm e}^{-2 x^{3} \ln \left (\frac {5}{4}\right )}}{9}\) | \(12\) |
derivativedivides | \(\frac {25 \,{\mathrm e}^{-2 x^{3} \ln \left (\frac {5}{4}\right )}}{9}\) | \(12\) |
default | \(\frac {25 \,{\mathrm e}^{-2 x^{3} \ln \left (\frac {5}{4}\right )}}{9}\) | \(12\) |
norman | \(\frac {25 \,{\mathrm e}^{-2 x^{3} \ln \left (\frac {5}{4}\right )}}{9}\) | \(12\) |
risch | \(-\frac {\left (-\frac {50 \ln \left (5\right )}{3}+\frac {100 \ln \left (2\right )}{3}\right ) 5^{-2 x^{3}} 4^{2 x^{3}}}{6 \left (\ln \left (5\right )-2 \ln \left (2\right )\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (11) = 22\).
time = 0.26, size = 48, normalized size = 2.40 \begin {gather*} -\frac {5^{2 \, {\left (x^{3} - 1\right )} {\left (\frac {2 \, \log \left (2\right )}{\log \left (5\right )} - 1\right )} + \frac {4 \, \log \left (2\right )}{\log \left (5\right )}} \log \left (\frac {5}{4}\right )}{9 \, {\left (\frac {2 \, \log \left (2\right )}{\log \left (5\right )} - 1\right )} \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 11, normalized size = 0.55 \begin {gather*} \frac {25}{9 \, \left (\frac {5}{4}\right )^{2 \, x^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 14, normalized size = 0.70 \begin {gather*} \frac {25 e^{- 2 x^{3} \log {\left (\frac {5}{4} \right )}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 22, normalized size = 1.10 \begin {gather*} \frac {25 \, \log \left (\frac {5}{4}\right )}{9 \, \left (\frac {5}{4}\right )^{2 \, x^{3}} {\left (\log \left (5\right ) - 2 \, \log \left (2\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 11, normalized size = 0.55 \begin {gather*} \frac {25}{9\,{\left (\frac {5}{4}\right )}^{2\,x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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