Optimal. Leaf size=24 \[ 5 \log \left (2+e^{e^8 x^8+\frac {1}{5} \left (x+x^2\right )}\right ) \]
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Rubi [A]
time = 0.13, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6816}
\begin {gather*} 5 \log \left (e^{\frac {1}{5} \left (5 e^8 x^8+x^2+x\right )}+2\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=5 \log \left (2+e^{\frac {1}{5} \left (x+x^2+5 e^8 x^8\right )}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 23, normalized size = 0.96 \begin {gather*} 5 \log \left (2+e^{\frac {1}{5} x \left (1+x+5 e^8 x^7\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.21, size = 20, normalized size = 0.83
method | result | size |
risch | \(5 \ln \left ({\mathrm e}^{\frac {x \left (5 x^{7} {\mathrm e}^{8}+x +1\right )}{5}}+2\right )\) | \(20\) |
norman | \(5 \ln \left ({\mathrm e}^{x^{8} {\mathrm e}^{8}+\frac {x^{2}}{5}+\frac {x}{5}}+2\right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 37, normalized size = 1.54 \begin {gather*} x^{2} + x + 5 \, \log \left ({\left (e^{\left (x^{8} e^{8} + \frac {1}{5} \, x^{2} + \frac {1}{5} \, x\right )} + 2\right )} e^{\left (-\frac {1}{5} \, x^{2} - \frac {1}{5} \, x\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 21, normalized size = 0.88 \begin {gather*} 5 \, \log \left (e^{\left (x^{8} e^{8} + \frac {1}{5} \, x^{2} + \frac {1}{5} \, x\right )} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 20, normalized size = 0.83 \begin {gather*} 5 \log {\left (e^{x^{8} e^{8} + \frac {x^{2}}{5} + \frac {x}{5}} + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 21, normalized size = 0.88 \begin {gather*} 5 \, \log \left (e^{\left (x^{8} e^{8} + \frac {1}{5} \, x^{2} + \frac {1}{5} \, x\right )} + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 23, normalized size = 0.96 \begin {gather*} \ln \left ({\left ({\mathrm {e}}^{x^8\,{\mathrm {e}}^8}\,{\mathrm {e}}^{x/5}\,{\mathrm {e}}^{\frac {x^2}{5}}+2\right )}^5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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