Optimal. Leaf size=25 \[ \frac {1}{2 x \left (\frac {7}{2}-2 x+\log \left (x+\log \left (2 x^2\right )\right )\right )} \]
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Rubi [A]
time = 0.37, antiderivative size = 22, normalized size of antiderivative = 0.88, number of steps
used = 2, number of rules used = 2, integrand size = 154, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6820, 6819}
\begin {gather*} \frac {1}{x \left (2 \log \left (\log \left (2 x^2\right )+x\right )-4 x+7\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6819
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4-9 x+8 x^2+\log \left (2 x^2\right ) \left (-7+8 x-2 \log \left (x+\log \left (2 x^2\right )\right )\right )-2 x \log \left (x+\log \left (2 x^2\right )\right )}{x^2 \left (x+\log \left (2 x^2\right )\right ) \left (7-4 x+2 \log \left (x+\log \left (2 x^2\right )\right )\right )^2} \, dx\\ &=\frac {1}{x \left (7-4 x+2 \log \left (x+\log \left (2 x^2\right )\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.21, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{x \left (7-4 x+2 \log \left (x+\log \left (2 x^2\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 7.38, size = 0, normalized size = 0.00 \[\int \frac {\left (-2 \ln \left (2 x^{2}\right )-2 x \right ) \ln \left (\ln \left (2 x^{2}\right )+x \right )+\left (8 x -7\right ) \ln \left (2 x^{2}\right )+8 x^{2}-9 x -4}{\left (4 x^{2} \ln \left (2 x^{2}\right )+4 x^{3}\right ) \ln \left (\ln \left (2 x^{2}\right )+x \right )^{2}+\left (\left (-16 x^{3}+28 x^{2}\right ) \ln \left (2 x^{2}\right )-16 x^{4}+28 x^{3}\right ) \ln \left (\ln \left (2 x^{2}\right )+x \right )+\left (16 x^{4}-56 x^{3}+49 x^{2}\right ) \ln \left (2 x^{2}\right )+16 x^{5}-56 x^{4}+49 x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.53, size = 25, normalized size = 1.00 \begin {gather*} -\frac {1}{4 \, x^{2} - 2 \, x \log \left (x + \log \left (2\right ) + 2 \, \log \left (x\right )\right ) - 7 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 25, normalized size = 1.00 \begin {gather*} -\frac {1}{4 \, x^{2} - 2 \, x \log \left (x + \log \left (2 \, x^{2}\right )\right ) - 7 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{- 4 x^{2} + 2 x \log {\left (x + \log {\left (2 x^{2} \right )} \right )} + 7 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 25, normalized size = 1.00 \begin {gather*} -\frac {1}{4 \, x^{2} - 2 \, x \log \left (x + \log \left (2 \, x^{2}\right )\right ) - 7 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.48, size = 22, normalized size = 0.88 \begin {gather*} \frac {1}{x\,\left (2\,\ln \left (x+\ln \left (2\,x^2\right )\right )-4\,x+7\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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