Optimal. Leaf size=23 \[ \frac {1}{2} \left (-\frac {8 e^{x^2}}{5}-\frac {64}{9 x^2}+\log (x)\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 14, 2209} \begin {gather*} -\frac {4 e^{x^2}}{5}-\frac {32}{9 x^2}+\frac {\log (x)}{2} \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}{90} \int \frac {640+45 x^2-144 e^{x^2} x^4}{x^3} \, dx\\ &=\frac {1}{90} \int \left (-144 e^{x^2} x+\frac {5 \left (128+9 x^2\right )}{x^3}\right ) \, dx\\ &=\frac {1}{18} \int \frac {128+9 x^2}{x^3} \, dx-\frac {8}{5} \int e^{x^2} x \, dx\\ &=-\frac {4 e^{x^2}}{5}+\frac {1}{18} \int \left (\frac {128}{x^3}+\frac {9}{x}\right ) \, dx\\ &=-\frac {4 e^{x^2}}{5}-\frac {32}{9 x^2}+\frac {\log (x)}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} -\frac {4 e^{x^2}}{5}-\frac {32}{9 x^2}+\frac {\log (x)}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 23, normalized size = 1.00 \begin {gather*} -\frac {72 \, x^{2} e^{\left (x^{2}\right )} - 45 \, x^{2} \log \relax (x) + 320}{90 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 25, normalized size = 1.09 \begin {gather*} -\frac {144 \, x^{2} e^{\left (x^{2}\right )} - 45 \, x^{2} \log \left (x^{2}\right ) + 640}{180 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.74
method | result | size |
default | \(\frac {\ln \relax (x )}{2}-\frac {32}{9 x^{2}}-\frac {4 \,{\mathrm e}^{x^{2}}}{5}\) | \(17\) |
risch | \(\frac {\ln \relax (x )}{2}-\frac {32}{9 x^{2}}-\frac {4 \,{\mathrm e}^{x^{2}}}{5}\) | \(17\) |
norman | \(\frac {-\frac {32}{9}-\frac {4 x^{2} {\mathrm e}^{x^{2}}}{5}}{x^{2}}+\frac {\ln \relax (x )}{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 16, normalized size = 0.70 \begin {gather*} -\frac {32}{9 \, x^{2}} - \frac {4}{5} \, e^{\left (x^{2}\right )} + \frac {1}{2} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 21, normalized size = 0.91 \begin {gather*} \frac {\ln \relax (x)}{2}-\frac {72\,x^2\,{\mathrm {e}}^{x^2}+320}{90\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 19, normalized size = 0.83 \begin {gather*} - \frac {4 e^{x^{2}}}{5} + \frac {\log {\relax (x )}}{2} - \frac {32}{9 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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