Optimal. Leaf size=23 \[ e^{-2+e^x+\frac {x^2}{3 \left (3+\frac {9}{x}\right )}} \]
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Rubi [A]
time = 0.53, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps
used = 3, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {27, 12, 6838}
\begin {gather*} e^{\frac {x^3}{9 (x+3)}+e^x-2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-2+e^x+\frac {x^3}{27+9 x}} \left (9 x^2+2 x^3+e^x \left (81+54 x+9 x^2\right )\right )}{9 (3+x)^2} \, dx\\ &=\frac {1}{9} \int \frac {e^{-2+e^x+\frac {x^3}{27+9 x}} \left (9 x^2+2 x^3+e^x \left (81+54 x+9 x^2\right )\right )}{(3+x)^2} \, dx\\ &=e^{-2+e^x+\frac {x^3}{9 (3+x)}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 23, normalized size = 1.00 \begin {gather*} e^{e^x+\frac {-54-18 x+x^3}{9 (3+x)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.48, size = 26, normalized size = 1.13
method | result | size |
risch | \({\mathrm e}^{\frac {x^{3}+9 \,{\mathrm e}^{x} x +27 \,{\mathrm e}^{x}-18 x -54}{9 x +27}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 23, normalized size = 1.00 \begin {gather*} e^{\left (\frac {x^{3} + 9 \, {\left (x + 3\right )} e^{x} - 18 \, x - 54}{9 \, {\left (x + 3\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 5.95, size = 15, normalized size = 0.65 \begin {gather*} e^{\frac {x^{3}}{9 x + 27}} e^{e^{x} - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 45 vs.
\(2 (19) = 38\).
time = 0.42, size = 45, normalized size = 1.96 \begin {gather*} e^{\left (\frac {x^{3}}{9 \, {\left (x + 3\right )}} + \frac {x e^{x}}{x + 3} - \frac {2 \, x}{x + 3} + \frac {3 \, e^{x}}{x + 3} - \frac {6}{x + 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.29, size = 18, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{\frac {x^3}{9\,x+27}}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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