Optimal. Leaf size=22 \[ -5-\frac {x}{3}-4 e^x x+x \left (-\frac {2}{x}+x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2207, 2225}
\begin {gather*} x^2-\frac {x}{3}+4 e^x-4 e^x (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-1+e^x (-12-12 x)+6 x\right ) \, dx\\ &=-\frac {x}{3}+x^2+\frac {1}{3} \int e^x (-12-12 x) \, dx\\ &=-\frac {x}{3}+x^2-4 e^x (1+x)+4 \int e^x \, dx\\ &=4 e^x-\frac {x}{3}+x^2-4 e^x (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.68 \begin {gather*} -\frac {x}{3}-4 e^x x+x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 13, normalized size = 0.59
method | result | size |
default | \(-\frac {x}{3}+x^{2}-4 \,{\mathrm e}^{x} x\) | \(13\) |
norman | \(-\frac {x}{3}+x^{2}-4 \,{\mathrm e}^{x} x\) | \(13\) |
risch | \(-\frac {x}{3}+x^{2}-4 \,{\mathrm e}^{x} x\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 12, normalized size = 0.55 \begin {gather*} x^{2} - 4 \, x e^{x} - \frac {1}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 12, normalized size = 0.55 \begin {gather*} x^{2} - 4 \, x e^{x} - \frac {1}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.55 \begin {gather*} x^{2} - 4 x e^{x} - \frac {x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 12, normalized size = 0.55 \begin {gather*} x^{2} - 4 \, x e^{x} - \frac {1}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 12, normalized size = 0.55 \begin {gather*} -\frac {x\,\left (12\,{\mathrm {e}}^x-3\,x+1\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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