Optimal. Leaf size=29 \[ \frac {3-e^{\frac {3}{2}-x}}{3 \left (-3+16 e^x\right ) x} \]
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Rubi [F] time = 1.06, 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 {9+e^{\frac {1}{2} (3-2 x)} (-3-3 x)+e^x \left (-48-48 x+e^{\frac {1}{2} (3-2 x)} (16+32 x)\right )}{27 x^2-288 e^x x^2+768 e^{2 x} x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9+e^{\frac {1}{2} (3-2 x)} (-3-3 x)+e^x \left (-48-48 x+e^{\frac {1}{2} (3-2 x)} (16+32 x)\right )}{3 \left (3-16 e^x\right )^2 x^2} \, dx\\ &=\frac {1}{3} \int \frac {9+e^{\frac {1}{2} (3-2 x)} (-3-3 x)+e^x \left (-48-48 x+e^{\frac {1}{2} (3-2 x)} (16+32 x)\right )}{\left (3-16 e^x\right )^2 x^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {-9+16 e^{3/2}}{\left (-3+16 e^x\right )^2 x}-\frac {e^{\frac {3}{2}-x} (1+x)}{3 x^2}+\frac {\left (-9+16 e^{3/2}\right ) (1+x)}{3 \left (-3+16 e^x\right ) x^2}\right ) \, dx\\ &=-\left (\frac {1}{9} \int \frac {e^{\frac {3}{2}-x} (1+x)}{x^2} \, dx\right )+\frac {1}{9} \left (-9+16 e^{3/2}\right ) \int \frac {1+x}{\left (-3+16 e^x\right ) x^2} \, dx+\frac {1}{3} \left (-9+16 e^{3/2}\right ) \int \frac {1}{\left (-3+16 e^x\right )^2 x} \, dx\\ &=\frac {e^{\frac {3}{2}-x}}{9 x}+\frac {1}{9} \left (-9+16 e^{3/2}\right ) \int \left (\frac {1}{\left (-3+16 e^x\right ) x^2}+\frac {1}{\left (-3+16 e^x\right ) x}\right ) \, dx+\frac {1}{3} \left (-9+16 e^{3/2}\right ) \int \frac {1}{\left (-3+16 e^x\right )^2 x} \, dx\\ &=\frac {e^{\frac {3}{2}-x}}{9 x}+\frac {1}{9} \left (-9+16 e^{3/2}\right ) \int \frac {1}{\left (-3+16 e^x\right ) x^2} \, dx+\frac {1}{9} \left (-9+16 e^{3/2}\right ) \int \frac {1}{\left (-3+16 e^x\right ) x} \, dx+\frac {1}{3} \left (-9+16 e^{3/2}\right ) \int \frac {1}{\left (-3+16 e^x\right )^2 x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.74, size = 29, normalized size = 1.00 \begin {gather*} -\frac {3-e^{\frac {3}{2}-x}}{3 \left (3 x-16 e^x x\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 24, normalized size = 0.83 \begin {gather*} -\frac {e^{\frac {3}{2}} - 3 \, e^{x}}{3 \, {\left (16 \, x e^{\left (2 \, x\right )} - 3 \, x e^{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 24, normalized size = 0.83 \begin {gather*} -\frac {e^{\frac {3}{2}} - 3 \, e^{x}}{3 \, {\left (16 \, x e^{\left (2 \, x\right )} - 3 \, x e^{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 24, normalized size = 0.83
method | result | size |
norman | \(\frac {\left (-\frac {{\mathrm e}^{\frac {3}{2}}}{3}+{\mathrm e}^{x}\right ) {\mathrm e}^{-x}}{x \left (16 \,{\mathrm e}^{x}-3\right )}\) | \(24\) |
risch | \(\frac {{\mathrm e}^{\frac {3}{2}-x}}{9 x}-\frac {16 \,{\mathrm e}^{\frac {3}{2}}-9}{9 x \left (16 \,{\mathrm e}^{x}-3\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 11, normalized size = 0.38 \begin {gather*} \frac {1}{16 \, x e^{x} - 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 24, normalized size = 0.83 \begin {gather*} -\frac {{\mathrm {e}}^{-x}\,\left ({\mathrm {e}}^{3/2}-3\,{\mathrm {e}}^x\right )}{3\,x\,\left (16\,{\mathrm {e}}^x-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 29, normalized size = 1.00 \begin {gather*} \frac {9 - 16 e^{\frac {3}{2}}}{144 x e^{x} - 27 x} + \frac {e^{\frac {3}{2}} e^{- x}}{9 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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