Optimal. Leaf size=17 \[ 16 e^{20 x \left (5-\left (12+e^x\right ) x\right )} \]
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Rubi [A]
time = 0.15, antiderivative size = 21, normalized size of antiderivative = 1.24, number of steps
used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6838}
\begin {gather*} 16 e^{-20 e^x x^2-240 x^2+100 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 e^{100 x-240 x^2-20 e^x x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 16, normalized size = 0.94 \begin {gather*} 16 e^{-20 x \left (-5+\left (12+e^x\right ) x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 16, normalized size = 0.94
method | result | size |
risch | \(16 \,{\mathrm e}^{-20 x \left ({\mathrm e}^{x} x +12 x -5\right )}\) | \(16\) |
norman | \(16 \,{\mathrm e}^{-20 \,{\mathrm e}^{x} x^{2}-240 x^{2}+100 x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 120.24, size = 19, normalized size = 1.12 \begin {gather*} 16 \, e^{\left (-20 \, x^{2} e^{x} - 240 \, x^{2} + 100 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 19, normalized size = 1.12 \begin {gather*} 16 \, e^{\left (-20 \, x^{2} e^{x} - 240 \, x^{2} + 100 \, 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 = 1.12 \begin {gather*} 16 e^{- 20 x^{2} e^{x} - 240 x^{2} + 100 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 19, normalized size = 1.12 \begin {gather*} 16 \, e^{\left (-20 \, x^{2} e^{x} - 240 \, x^{2} + 100 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.24, size = 20, normalized size = 1.18 \begin {gather*} 16\,{\mathrm {e}}^{100\,x}\,{\mathrm {e}}^{-20\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-240\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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