Optimal. Leaf size=24 \[ e^{\frac {1}{4} \left (-\frac {17}{9}+e^x\right ) \left (-e^{x/4}+x\right )} \]
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Rubi [F]
time = 1.11, 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}{144} \exp \left (\frac {1}{36} \left (17 e^{x/4}-17 x+e^x \left (-9 e^{x/4}+9 x\right )\right )\right ) \left (-68+17 e^{x/4}+e^x \left (36-45 e^{x/4}+36 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}{144} \int \exp \left (\frac {1}{36} \left (17 e^{x/4}-17 x+e^x \left (-9 e^{x/4}+9 x\right )\right )\right ) \left (-68+17 e^{x/4}+e^x \left (36-45 e^{x/4}+36 x\right )\right ) \, dx\\ &=\frac {1}{36} \text {Subst}\left (\int e^{-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )} \left (-68+17 e^x+e^{4 x} \left (36-45 e^x+144 x\right )\right ) \, dx,x,\frac {x}{4}\right )\\ &=\frac {1}{36} \text {Subst}\left (\int \left (-68 e^{-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )}+17 \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+x\right )-9 \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right ) \left (-4+5 e^x-16 x\right )\right ) \, dx,x,\frac {x}{4}\right )\\ &=-\left (\frac {1}{4} \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right ) \left (-4+5 e^x-16 x\right ) \, dx,x,\frac {x}{4}\right )\right )+\frac {17}{36} \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+x\right ) \, dx,x,\frac {x}{4}\right )-\frac {17}{9} \text {Subst}\left (\int e^{-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )} \, dx,x,\frac {x}{4}\right )\\ &=-\left (\frac {1}{4} \text {Subst}\left (\int \left (-4 \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right )+5 \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+5 x\right )-16 \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right ) x\right ) \, dx,x,\frac {x}{4}\right )\right )+\frac {17}{36} \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+x\right ) \, dx,x,\frac {x}{4}\right )-\frac {17}{9} \text {Subst}\left (\int e^{-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )} \, dx,x,\frac {x}{4}\right )\\ &=\frac {17}{36} \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+x\right ) \, dx,x,\frac {x}{4}\right )-\frac {5}{4} \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+5 x\right ) \, dx,x,\frac {x}{4}\right )-\frac {17}{9} \text {Subst}\left (\int e^{-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )} \, dx,x,\frac {x}{4}\right )+4 \text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right ) x \, dx,x,\frac {x}{4}\right )+\text {Subst}\left (\int \exp \left (-\frac {1}{36} \left (-17+9 e^{4 x}\right ) \left (e^x-4 x\right )+4 x\right ) \, dx,x,\frac {x}{4}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.25, size = 24, normalized size = 1.00 \begin {gather*} e^{-\frac {1}{36} \left (-17+9 e^x\right ) \left (e^{x/4}-x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 18, normalized size = 0.75
method | result | size |
risch | \({\mathrm e}^{\frac {\left (x -{\mathrm e}^{\frac {x}{4}}\right ) \left (9 \,{\mathrm e}^{x}-17\right )}{36}}\) | \(18\) |
norman | \({\mathrm e}^{\frac {\left (-9 \,{\mathrm e}^{\frac {x}{4}}+9 x \right ) {\mathrm e}^{x}}{36}+\frac {17 \,{\mathrm e}^{\frac {x}{4}}}{36}-\frac {17 x}{36}}\) | \(30\) |
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 = 22, normalized size = 0.92 \begin {gather*} e^{\left (\frac {1}{4} \, x e^{x} - \frac {17}{36} \, x - \frac {1}{4} \, e^{\left (\frac {5}{4} \, x\right )} + \frac {17}{36} \, e^{\left (\frac {1}{4} \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 27, normalized size = 1.12 \begin {gather*} e^{- \frac {17 x}{36} + \left (\frac {x}{4} - \frac {e^{\frac {x}{4}}}{4}\right ) e^{x} + \frac {17 e^{\frac {x}{4}}}{36}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 22, normalized size = 0.92 \begin {gather*} e^{\left (\frac {1}{4} \, x e^{x} - \frac {17}{36} \, x - \frac {1}{4} \, e^{\left (\frac {5}{4} \, x\right )} + \frac {17}{36} \, e^{\left (\frac {1}{4} \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.30, size = 27, normalized size = 1.12 \begin {gather*} {\mathrm {e}}^{\frac {17\,{\mathrm {e}}^{x/4}}{36}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{4}}\,{\mathrm {e}}^{-\frac {17\,x}{36}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{x/4}\,{\mathrm {e}}^x}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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