Optimal. Leaf size=18 \[ 4^{\left (-\frac {1}{3}+x\right ) x^2 \left (6-x^2\right )} \]
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Rubi [A]
time = 0.11, antiderivative size = 36, normalized size of antiderivative = 2.00, number of steps
used = 2, number of rules used = 2, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {12, 6838}
\begin {gather*} \frac {2^{-\frac {2}{3} \left (3 x^5-x^4-18 x^3+6 x^2\right )-1} \log (4)}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \log (4) \int 2^{\frac {2}{3} \left (-6 x^2+18 x^3+x^4-3 x^5\right )} \left (-12 x+54 x^2+4 x^3-15 x^4\right ) \, dx\\ &=\frac {2^{-1-\frac {2}{3} \left (6 x^2-18 x^3-x^4+3 x^5\right )} \log (4)}{\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 1.15, size = 33, normalized size = 1.83 \begin {gather*} \frac {2^{-1-4 x^2+12 x^3+\frac {2 x^4}{3}-2 x^5} \log (4)}{\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 25, normalized size = 1.39
method | result | size |
risch | \(2^{-\frac {2 x^{2} \left (3 x -1\right ) \left (x^{2}-6\right )}{3}}\) | \(18\) |
gosper | \({\mathrm e}^{-\frac {2 x^{2} \left (3 x^{3}-x^{2}-18 x +6\right ) \ln \left (2\right )}{3}}\) | \(24\) |
derivativedivides | \({\mathrm e}^{\frac {2 \left (-3 x^{5}+x^{4}+18 x^{3}-6 x^{2}\right ) \ln \left (2\right )}{3}}\) | \(25\) |
default | \({\mathrm e}^{\frac {2 \left (-3 x^{5}+x^{4}+18 x^{3}-6 x^{2}\right ) \ln \left (2\right )}{3}}\) | \(25\) |
norman | \({\mathrm e}^{\frac {2 \left (-3 x^{5}+x^{4}+18 x^{3}-6 x^{2}\right ) \ln \left (2\right )}{3}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 1.28 \begin {gather*} 2^{-2 \, x^{5} + \frac {2}{3} \, x^{4} + 12 \, x^{3} - 4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 23, normalized size = 1.28 \begin {gather*} 2^{-2 \, x^{5} + \frac {2}{3} \, x^{4} + 12 \, x^{3} - 4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 26, normalized size = 1.44 \begin {gather*} e^{\left (- 2 x^{5} + \frac {2 x^{4}}{3} + 12 x^{3} - 4 x^{2}\right ) \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 23, normalized size = 1.28 \begin {gather*} 2^{-2 \, x^{5} + \frac {2}{3} \, x^{4} + 12 \, x^{3} - 4 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.16, size = 33, normalized size = 1.83 \begin {gather*} \frac {2^{\frac {2\,x^4}{3}}\,2^{12\,x^3}}{2^{4\,x^2}\,2^{2\,x^5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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