Optimal. Leaf size=25 \[ \frac {25}{3} \left (1-e^{x^2}-x\right )+\frac {3}{\log (2 x)} \]
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Rubi [A] time = 0.24, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps used = 6, number of rules used = 5, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.139, Rules used = {12, 6688, 2209, 2302, 30} \begin {gather*} -\frac {25 e^{x^2}}{3}-\frac {25 x}{3}+\frac {3}{\log (2 x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2209
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {-9+\left (-25 x-50 e^{x^2} x^2\right ) \log ^2(2 x)}{x \log ^2(2 x)} \, dx\\ &=\frac {1}{3} \int \left (-25-50 e^{x^2} x-\frac {9}{x \log ^2(2 x)}\right ) \, dx\\ &=-\frac {25 x}{3}-3 \int \frac {1}{x \log ^2(2 x)} \, dx-\frac {50}{3} \int e^{x^2} x \, dx\\ &=-\frac {25 e^{x^2}}{3}-\frac {25 x}{3}-3 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (2 x)\right )\\ &=-\frac {25 e^{x^2}}{3}-\frac {25 x}{3}+\frac {3}{\log (2 x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 0.92 \begin {gather*} -\frac {25 e^{x^2}}{3}-\frac {25 x}{3}+\frac {3}{\log (2 x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 22, normalized size = 0.88 \begin {gather*} -\frac {25 \, {\left (x + e^{\left (x^{2}\right )}\right )} \log \left (2 \, x\right ) - 9}{3 \, \log \left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 27, normalized size = 1.08 \begin {gather*} -\frac {25 \, x \log \left (2 \, x\right ) + 25 \, e^{\left (x^{2}\right )} \log \left (2 \, x\right ) - 9}{3 \, \log \left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 19, normalized size = 0.76
method | result | size |
default | \(-\frac {25 x}{3}+\frac {3}{\ln \left (2 x \right )}-\frac {25 \,{\mathrm e}^{x^{2}}}{3}\) | \(19\) |
risch | \(-\frac {25 x}{3}+\frac {3}{\ln \left (2 x \right )}-\frac {25 \,{\mathrm e}^{x^{2}}}{3}\) | \(19\) |
norman | \(\frac {3-\frac {25 x \ln \left (2 x \right )}{3}-\frac {25 \,{\mathrm e}^{x^{2}} \ln \left (2 x \right )}{3}}{\ln \left (2 x \right )}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 18, normalized size = 0.72 \begin {gather*} -\frac {25}{3} \, x + \frac {3}{\log \left (2 \, x\right )} - \frac {25}{3} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.40, size = 18, normalized size = 0.72 \begin {gather*} \frac {3}{\ln \left (2\,x\right )}-\frac {25\,{\mathrm {e}}^{x^2}}{3}-\frac {25\,x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 19, normalized size = 0.76 \begin {gather*} - \frac {25 x}{3} - \frac {25 e^{x^{2}}}{3} + \frac {3}{\log {\left (2 x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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