Optimal. Leaf size=19 \[ e^{-\frac {27}{2} e^{-x} (-25+x) x} x^2 \]
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Rubi [F]
time = 0.62, 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}{2} e^{-x-\frac {1}{2} e^{-x} \left (-675 x+27 x^2\right )} \left (4 e^x x+675 x^2-729 x^3+27 x^4\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}{2} \int e^{-x-\frac {1}{2} e^{-x} \left (-675 x+27 x^2\right )} \left (4 e^x x+675 x^2-729 x^3+27 x^4\right ) \, dx\\ &=\frac {1}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} \left (4 e^x x+675 x^2-729 x^3+27 x^4\right ) \, dx\\ &=\frac {1}{2} \int \left (4 e^{x-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x+675 e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^2-729 e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^3+27 e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^4\right ) \, dx\\ &=2 \int e^{x-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x \, dx+\frac {27}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^4 \, dx+\frac {675}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^2 \, dx-\frac {729}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^3 \, dx\\ &=2 \int e^{-\frac {27}{2} e^{-x} (-25+x) x} x \, dx+\frac {27}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^4 \, dx+\frac {675}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^2 \, dx-\frac {729}{2} \int e^{-\frac {1}{2} e^{-x} x \left (-675+2 e^x+27 x\right )} x^3 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 19, normalized size = 1.00 \begin {gather*} e^{-\frac {27}{2} e^{-x} (-25+x) x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 16, normalized size = 0.84
method | result | size |
risch | \(x^{2} {\mathrm e}^{-\frac {27 x \left (x -25\right ) {\mathrm e}^{-x}}{2}}\) | \(16\) |
norman | \(x^{2} {\mathrm e}^{-\frac {\left (27 x^{2}-675 x \right ) {\mathrm e}^{-x}}{2}}\) | \(23\) |
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 = 0.41, size = 27, normalized size = 1.42 \begin {gather*} x^{2} e^{\left (-\frac {1}{2} \, {\left (27 \, x^{2} + 2 \, x e^{x} - 675 \, x\right )} e^{\left (-x\right )} + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 19, normalized size = 1.00 \begin {gather*} x^{2} e^{- \left (\frac {27 x^{2}}{2} - \frac {675 x}{2}\right ) e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.52, size = 22, normalized size = 1.16 \begin {gather*} x^2\,{\mathrm {e}}^{\frac {675\,x\,{\mathrm {e}}^{-x}}{2}}\,{\mathrm {e}}^{-\frac {27\,x^2\,{\mathrm {e}}^{-x}}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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