Optimal. Leaf size=24 \[ 3 x \left (-e^{\frac {-2 x+x \left (\frac {7}{2}+x\right )}{x}}+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 35, normalized size of antiderivative = 1.46, number of steps used = 3, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2176, 2194} \begin {gather*} 3 x^2+3 e^{\frac {1}{2} (2 x+3)}-3 e^{\frac {1}{2} (2 x+3)} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 x^2+\int e^{\frac {1}{2} (3+2 x)} (-3-3 x) \, dx\\ &=3 x^2-3 e^{\frac {1}{2} (3+2 x)} (1+x)+3 \int e^{\frac {1}{2} (3+2 x)} \, dx\\ &=3 e^{\frac {1}{2} (3+2 x)}+3 x^2-3 e^{\frac {1}{2} (3+2 x)} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.67 \begin {gather*} -3 e^{\frac {3}{2}+x} x+3 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 13, normalized size = 0.54 \begin {gather*} 3 \, x^{2} - 3 \, x e^{\left (x + \frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 13, normalized size = 0.54 \begin {gather*} 3 \, x^{2} - 3 \, x e^{\left (x + \frac {3}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.58
method | result | size |
norman | \(3 x^{2}-3 \,{\mathrm e}^{x +\frac {3}{2}} x\) | \(14\) |
risch | \(3 x^{2}-3 \,{\mathrm e}^{x +\frac {3}{2}} x\) | \(14\) |
default | \(-3 \,{\mathrm e}^{x +\frac {3}{2}} \left (x +\frac {3}{2}\right )+\frac {9 \,{\mathrm e}^{x +\frac {3}{2}}}{2}+3 x^{2}\) | \(22\) |
derivativedivides | \(-9 x -\frac {27}{2}-3 \,{\mathrm e}^{x +\frac {3}{2}} \left (x +\frac {3}{2}\right )+\frac {9 \,{\mathrm e}^{x +\frac {3}{2}}}{2}+3 \left (x +\frac {3}{2}\right )^{2}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 25, normalized size = 1.04 \begin {gather*} 3 \, x^{2} - 3 \, {\left (x e^{\frac {3}{2}} - e^{\frac {3}{2}}\right )} e^{x} - 3 \, e^{\left (x + \frac {3}{2}\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 = 0.54 \begin {gather*} 3\,x^2-3\,x\,{\mathrm {e}}^{3/2}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.58 \begin {gather*} 3 x^{2} - 3 x e^{x + \frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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