Optimal. Leaf size=24 \[ \frac {e^4}{e^x-\frac {25 e^5 x^3}{9}-\log (8)} \]
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Rubi [A] time = 0.18, antiderivative size = 25, normalized size of antiderivative = 1.04, number of steps used = 2, number of rules used = 2, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6688, 6686} \begin {gather*} \frac {9 e^4}{-25 e^5 x^3+9 e^x-9 \log (8)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-81 e^{4+x}+675 e^9 x^2}{\left (9 e^x-25 e^5 x^3-9 \log (8)\right )^2} \, dx\\ &=\frac {9 e^4}{9 e^x-25 e^5 x^3-9 \log (8)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 25, normalized size = 1.04 \begin {gather*} -\frac {9 e^4}{-9 e^x+25 e^5 x^3+9 \log (8)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 26, normalized size = 1.08 \begin {gather*} -\frac {9 \, e^{8}}{25 \, x^{3} e^{9} + 27 \, e^{4} \log \relax (2) - 9 \, e^{\left (x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 23, normalized size = 0.96
method | result | size |
norman | \(-\frac {9 \,{\mathrm e}^{4}}{25 x^{3} {\mathrm e}^{5}-9 \,{\mathrm e}^{x}+27 \ln \relax (2)}\) | \(23\) |
risch | \(-\frac {9 \,{\mathrm e}^{4}}{25 x^{3} {\mathrm e}^{5}-9 \,{\mathrm e}^{x}+27 \ln \relax (2)}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 22, normalized size = 0.92 \begin {gather*} -\frac {9 \, e^{4}}{25 \, x^{3} e^{5} - 9 \, e^{x} + 27 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.18, size = 22, normalized size = 0.92 \begin {gather*} -\frac {9\,{\mathrm {e}}^4}{27\,\ln \relax (2)-9\,{\mathrm {e}}^x+25\,x^3\,{\mathrm {e}}^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.92 \begin {gather*} \frac {9 e^{4}}{- 25 x^{3} e^{5} + 9 e^{x} - 27 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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