Optimal. Leaf size=14 \[ e^{\frac {32}{9} (5-x) x}+x \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.21, number of steps used = 4, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2244, 2236} \begin {gather*} e^{\frac {160 x}{9}-\frac {32 x^2}{9}}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \left (9+e^{\frac {1}{9} \left (160 x-32 x^2\right )} (160-64 x)\right ) \, dx\\ &=x+\frac {1}{9} \int e^{\frac {1}{9} \left (160 x-32 x^2\right )} (160-64 x) \, dx\\ &=x+\frac {1}{9} \int e^{\frac {160 x}{9}-\frac {32 x^2}{9}} (160-64 x) \, dx\\ &=e^{\frac {160 x}{9}-\frac {32 x^2}{9}}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 17, normalized size = 1.21 \begin {gather*} e^{\frac {160 x}{9}-\frac {32 x^2}{9}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 12, normalized size = 0.86 \begin {gather*} x + e^{\left (-\frac {32}{9} \, x^{2} + \frac {160}{9} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 12, normalized size = 0.86 \begin {gather*} x + e^{\left (-\frac {32}{9} \, x^{2} + \frac {160}{9} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 0.71
method | result | size |
risch | \(x +{\mathrm e}^{-\frac {32 \left (x -5\right ) x}{9}}\) | \(10\) |
default | \(x +{\mathrm e}^{-\frac {32}{9} x^{2}+\frac {160}{9} x}\) | \(13\) |
norman | \(x +{\mathrm e}^{-\frac {32}{9} x^{2}+\frac {160}{9} x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 12, normalized size = 0.86 \begin {gather*} x + e^{\left (-\frac {32}{9} \, x^{2} + \frac {160}{9} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 12, normalized size = 0.86 \begin {gather*} x+{\mathrm {e}}^{\frac {160\,x}{9}-\frac {32\,x^2}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 1.00 \begin {gather*} x + e^{- \frac {32 x^{2}}{9} + \frac {160 x}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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