Optimal. Leaf size=19 \[ 1-e^{-3 x/2}-\frac {5 x}{2}+x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} x^2-\frac {5 x}{2}-e^{-3 x/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-5+3 e^{-3 x/2}+4 x\right ) \, dx\\ &=-\frac {5 x}{2}+x^2+\frac {3}{2} \int e^{-3 x/2} \, dx\\ &=-e^{-3 x/2}-\frac {5 x}{2}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.16 \begin {gather*} \frac {1}{2} \left (-2 e^{-3 x/2}-5 x+2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 13, normalized size = 0.68 \begin {gather*} x^{2} - \frac {5}{2} \, x - e^{\left (-\frac {3}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 13, normalized size = 0.68 \begin {gather*} x^{2} - \frac {5}{2} \, x - e^{\left (-\frac {3}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 14, normalized size = 0.74
method | result | size |
derivativedivides | \(-\frac {5 x}{2}+x^{2}-{\mathrm e}^{-\frac {3 x}{2}}\) | \(14\) |
default | \(-\frac {5 x}{2}+x^{2}-{\mathrm e}^{-\frac {3 x}{2}}\) | \(14\) |
norman | \(-\frac {5 x}{2}+x^{2}-{\mathrm e}^{-\frac {3 x}{2}}\) | \(14\) |
risch | \(-\frac {5 x}{2}+x^{2}-{\mathrm e}^{-\frac {3 x}{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 13, normalized size = 0.68 \begin {gather*} x^{2} - \frac {5}{2} \, x - e^{\left (-\frac {3}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 13, normalized size = 0.68 \begin {gather*} x^2-{\mathrm {e}}^{-\frac {3\,x}{2}}-\frac {5\,x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 15, normalized size = 0.79 \begin {gather*} x^{2} - \frac {5 x}{2} - e^{- \frac {3 x}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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