Optimal. Leaf size=30 \[ 2+e^{-2 x^3+\frac {8}{\log \left (-e^x-x+\log (5 (-3+x))\right )}} \]
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Rubi [A]
time = 1.78, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 171, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6820, 12,
6838} \begin {gather*} \exp \left (\frac {8}{\log \left (-x-e^x+\log (-5 (3-x))\right )}-2 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6820
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2 \exp \left (-2 x^3+\frac {8}{\log \left (-e^x-x+\log (5 (-3+x))\right )}\right ) \left (-3 x^2-\frac {4 \left (-4+e^x (-3+x)+x\right )}{(-3+x) \left (e^x+x-\log (5 (-3+x))\right ) \log ^2\left (-e^x-x+\log (5 (-3+x))\right )}\right ) \, dx\\ &=2 \int \exp \left (-2 x^3+\frac {8}{\log \left (-e^x-x+\log (5 (-3+x))\right )}\right ) \left (-3 x^2-\frac {4 \left (-4+e^x (-3+x)+x\right )}{(-3+x) \left (e^x+x-\log (5 (-3+x))\right ) \log ^2\left (-e^x-x+\log (5 (-3+x))\right )}\right ) \, dx\\ &=\exp \left (-2 x^3+\frac {8}{\log \left (-e^x-x+\log (-5 (3-x))\right )}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 28, normalized size = 0.93 \begin {gather*} e^{-2 x^3+\frac {8}{\log \left (-e^x-x+\log (5 (-3+x))\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 42, normalized size = 1.40
method | result | size |
risch | \({\mathrm e}^{-\frac {2 \left (x^{3} \ln \left (\ln \left (5 x -15\right )-{\mathrm e}^{x}-x \right )-4\right )}{\ln \left (\ln \left (5 x -15\right )-{\mathrm e}^{x}-x \right )}}\) | \(42\) |
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 = 0.62, size = 41, normalized size = 1.37 \begin {gather*} e^{\left (-\frac {2 \, {\left (x^{3} \log \left (-x - e^{x} + \log \left (5 \, x - 15\right )\right ) - 4\right )}}{\log \left (-x - e^{x} + \log \left (5 \, x - 15\right )\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [A]
time = 7.11, size = 26, normalized size = 0.87 \begin {gather*} e^{\left (-2 \, x^{3} + \frac {8}{\log \left (-x - e^{x} + \log \left (5 \, x - 15\right )\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 27, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{-2\,x^3}\,{\mathrm {e}}^{\frac {8}{\ln \left (\ln \left (5\,x-15\right )-x-{\mathrm {e}}^x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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