Optimal. Leaf size=25 \[ \frac {1}{3 \left (e^{-\frac {9 (-81+x)}{x}+2 x+x^2}+x\right )} \]
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Rubi [A] time = 0.55, antiderivative size = 29, normalized size of antiderivative = 1.16, number of steps used = 3, number of rules used = 3, integrand size = 96, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6688, 12, 6686} \begin {gather*} \frac {e^9}{3 \left (e^{x^2+2 x+\frac {729}{x}}+e^9 x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^9 \left (-e^9 x^2-e^{\frac {729}{x}+2 x+x^2} \left (-729+2 x^2+2 x^3\right )\right )}{3 x^2 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )^2} \, dx\\ &=\frac {1}{3} e^9 \int \frac {-e^9 x^2-e^{\frac {729}{x}+2 x+x^2} \left (-729+2 x^2+2 x^3\right )}{x^2 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )^2} \, dx\\ &=\frac {e^9}{3 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 29, normalized size = 1.16 \begin {gather*} \frac {e^9}{3 \left (e^{\frac {729}{x}+2 x+x^2}+e^9 x\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.42, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{3 \, {\left (x + e^{\left (\frac {x^{3} + 2 \, x^{2} - 9 \, x + 729}{x}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{3 \, {\left (x + e^{\left (\frac {x^{3} + 2 \, x^{2} - 9 \, x + 729}{x}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.84, size = 25, normalized size = 1.00
method | result | size |
norman | \(\frac {1}{3 x +3 \,{\mathrm e}^{\frac {x^{3}+2 x^{2}-9 x +729}{x}}}\) | \(25\) |
risch | \(\frac {1}{3 x +3 \,{\mathrm e}^{\frac {x^{3}+2 x^{2}-9 x +729}{x}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 24, normalized size = 0.96 \begin {gather*} \frac {e^{9}}{3 \, {\left (x e^{9} + e^{\left (x^{2} + 2 \, x + \frac {729}{x}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.44, size = 27, normalized size = 1.08 \begin {gather*} \frac {{\mathrm {e}}^9}{3\,x\,{\mathrm {e}}^9+3\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{729/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{3 x + 3 e^{\frac {x^{3} + 2 x^{2} - 9 x + 729}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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