Optimal. Leaf size=22 \[ e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )}-x \]
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Rubi [F]
time = 0.68, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {1}{3} \left (-3+e^{\frac {1}{3} \left (e^{2 x}-10 x+e^x (-5+2 x)\right )} \left (-10+2 e^{2 x}+e^x (-3+2 x)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-3+e^{\frac {1}{3} \left (e^{2 x}-10 x+e^x (-5+2 x)\right )} \left (-10+2 e^{2 x}+e^x (-3+2 x)\right )\right ) \, dx\\ &=-x+\frac {1}{3} \int e^{\frac {1}{3} \left (e^{2 x}-10 x+e^x (-5+2 x)\right )} \left (-10+2 e^{2 x}+e^x (-3+2 x)\right ) \, dx\\ &=-x+\frac {1}{3} \int e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \left (-10+2 e^{2 x}+e^x (-3+2 x)\right ) \, dx\\ &=-x+\frac {1}{3} \int \left (-10 e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )}+2 e^{2 x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )}+e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} (-3+2 x)\right ) \, dx\\ &=-x+\frac {1}{3} \int e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} (-3+2 x) \, dx+\frac {2}{3} \int e^{2 x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx-\frac {10}{3} \int e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx\\ &=-x+\frac {1}{3} \int \left (-3 e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )}+2 e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} x\right ) \, dx+\frac {2}{3} \int e^{2 x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx-\frac {10}{3} \int e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx\\ &=-x+\frac {2}{3} \int e^{2 x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx+\frac {2}{3} \int e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} x \, dx-\frac {10}{3} \int e^{\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx-\int e^{x+\frac {1}{3} \left (-5+e^x\right ) \left (e^x+2 x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 27, normalized size = 1.23 \begin {gather*} e^{-\frac {10 x}{3}+\frac {1}{3} e^x \left (-5+e^x+2 x\right )}-x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 25, normalized size = 1.14
method | result | size |
default | \(-x +{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{3}+\frac {\left (2 x -5\right ) {\mathrm e}^{x}}{3}-\frac {10 x}{3}}\) | \(25\) |
norman | \(-x +{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{3}+\frac {\left (2 x -5\right ) {\mathrm e}^{x}}{3}-\frac {10 x}{3}}\) | \(25\) |
risch | \(-x +{\mathrm e}^{\frac {{\mathrm e}^{2 x}}{3}+\frac {2 \,{\mathrm e}^{x} x}{3}-\frac {5 \,{\mathrm e}^{x}}{3}-\frac {10 x}{3}}\) | \(25\) |
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 = 0.37, size = 24, normalized size = 1.09 \begin {gather*} -x + e^{\left (\frac {1}{3} \, {\left (2 \, x - 5\right )} e^{x} - \frac {10}{3} \, x + \frac {1}{3} \, e^{\left (2 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 26, normalized size = 1.18 \begin {gather*} - x + e^{- \frac {10 x}{3} + \left (\frac {2 x}{3} - \frac {5}{3}\right ) e^{x} + \frac {e^{2 x}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 24, normalized size = 1.09 \begin {gather*} -x + e^{\left (\frac {2}{3} \, x e^{x} - \frac {10}{3} \, x + \frac {1}{3} \, e^{\left (2 \, x\right )} - \frac {5}{3} \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 24, normalized size = 1.09 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{3}-\frac {10\,x}{3}-\frac {5\,{\mathrm {e}}^x}{3}+\frac {2\,x\,{\mathrm {e}}^x}{3}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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