Optimal. Leaf size=25 \[ -\frac {4 \left (6+x+\left (-e+e^{\frac {x^2}{2}}\right ) x\right )}{3 x} \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 0.76, number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {12, 14, 2209} \begin {gather*} -\frac {4}{3} e^{\frac {x^2}{2}}-\frac {8}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {24-4 e^{\frac {x^2}{2}} x^3}{x^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {24}{x^2}-4 e^{\frac {x^2}{2}} x\right ) \, dx\\ &=-\frac {8}{x}-\frac {4}{3} \int e^{\frac {x^2}{2}} x \, dx\\ &=-\frac {4}{3} e^{\frac {x^2}{2}}-\frac {8}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.76 \begin {gather*} -\frac {4}{3} e^{\frac {x^2}{2}}-\frac {8}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 15, normalized size = 0.60 \begin {gather*} -\frac {4 \, {\left (x e^{\left (\frac {1}{2} \, x^{2}\right )} + 6\right )}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 15, normalized size = 0.60 \begin {gather*} -\frac {4 \, {\left (x e^{\left (\frac {1}{2} \, x^{2}\right )} + 6\right )}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 0.60
method | result | size |
default | \(-\frac {8}{x}-\frac {4 \,{\mathrm e}^{\frac {x^{2}}{2}}}{3}\) | \(15\) |
risch | \(-\frac {8}{x}-\frac {4 \,{\mathrm e}^{\frac {x^{2}}{2}}}{3}\) | \(15\) |
norman | \(\frac {-8-\frac {4 x \,{\mathrm e}^{\frac {x^{2}}{2}}}{3}}{x}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 14, normalized size = 0.56 \begin {gather*} -\frac {8}{x} - \frac {4}{3} \, e^{\left (\frac {1}{2} \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.42, size = 14, normalized size = 0.56 \begin {gather*} -\frac {4\,{\mathrm {e}}^{\frac {x^2}{2}}}{3}-\frac {8}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.56 \begin {gather*} - \frac {4 e^{\frac {x^{2}}{2}}}{3} - \frac {8}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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