Optimal. Leaf size=18 \[ \log \left (\left (-5+e^{\frac {x^3}{3}}\right )^2-x\right ) \]
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Rubi [A] time = 0.07, antiderivative size = 26, normalized size of antiderivative = 1.44, number of steps used = 1, number of rules used = 1, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6684} \begin {gather*} \log \left (-10 e^{\frac {x^3}{3}}+e^{\frac {2 x^3}{3}}-x+25\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (25-10 e^{\frac {x^3}{3}}+e^{\frac {2 x^3}{3}}-x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 26, normalized size = 1.44 \begin {gather*} \log \left (25-10 e^{\frac {x^3}{3}}+e^{\frac {2 x^3}{3}}-x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 20, normalized size = 1.11 \begin {gather*} \log \left (-x + e^{\left (\frac {2}{3} \, x^{3}\right )} - 10 \, e^{\left (\frac {1}{3} \, x^{3}\right )} + 25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 20, normalized size = 1.11 \begin {gather*} \log \left (x - e^{\left (\frac {2}{3} \, x^{3}\right )} + 10 \, e^{\left (\frac {1}{3} \, x^{3}\right )} - 25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 1.17
method | result | size |
risch | \(\ln \left ({\mathrm e}^{\frac {2 x^{3}}{3}}-10 \,{\mathrm e}^{\frac {x^{3}}{3}}-x +25\right )\) | \(21\) |
derivativedivides | \(\ln \left ({\mathrm e}^{\frac {2 x^{3}}{3}}-10 \,{\mathrm e}^{\frac {x^{3}}{3}}-x +25\right )\) | \(23\) |
default | \(\ln \left ({\mathrm e}^{\frac {2 x^{3}}{3}}-10 \,{\mathrm e}^{\frac {x^{3}}{3}}-x +25\right )\) | \(23\) |
norman | \(\ln \left (-{\mathrm e}^{\frac {2 x^{3}}{3}}+x +10 \,{\mathrm e}^{\frac {x^{3}}{3}}-25\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 20, normalized size = 1.11 \begin {gather*} \log \left (x - e^{\left (\frac {2}{3} \, x^{3}\right )} + 10 \, e^{\left (\frac {1}{3} \, x^{3}\right )} - 25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 20, normalized size = 1.11 \begin {gather*} \ln \left (x+10\,{\mathrm {e}}^{\frac {x^3}{3}}-{\mathrm {e}}^{\frac {2\,x^3}{3}}-25\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 20, normalized size = 1.11 \begin {gather*} \log {\left (- x + e^{\frac {2 x^{3}}{3}} - 10 e^{\frac {x^{3}}{3}} + 25 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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