Optimal. Leaf size=26 \[ \frac {2}{x \left (1+\frac {x^2}{\left (9+\frac {7 x}{4}\right ) \log (x)}\right )} \]
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Rubi [F] time = 0.73, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {288 x^2+56 x^3+\left (-864 x^2-112 x^3\right ) \log (x)+\left (-2592-1008 x-98 x^2\right ) \log ^2(x)}{16 x^6+\left (288 x^4+56 x^5\right ) \log (x)+\left (1296 x^2+504 x^3+49 x^4\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (4 x^2 (36+7 x)-8 x^2 (54+7 x) \log (x)-(36+7 x)^2 \log ^2(x)\right )}{\left (4 x^3+x (36+7 x) \log (x)\right )^2} \, dx\\ &=2 \int \frac {4 x^2 (36+7 x)-8 x^2 (54+7 x) \log (x)-(36+7 x)^2 \log ^2(x)}{\left (4 x^3+x (36+7 x) \log (x)\right )^2} \, dx\\ &=2 \int \left (-\frac {1}{x^2}+\frac {4 \left (1296+504 x+337 x^2+28 x^3\right )}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2}-\frac {144}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )}\right ) \, dx\\ &=\frac {2}{x}+8 \int \frac {1296+504 x+337 x^2+28 x^3}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2} \, dx-288 \int \frac {1}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )} \, dx\\ &=\frac {2}{x}+8 \int \left (-\frac {3420}{49 \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2}+\frac {193 x}{7 \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2}+\frac {4 x^2}{\left (4 x^2+36 \log (x)+7 x \log (x)\right )^2}+\frac {186624}{49 (36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2}\right ) \, dx-288 \int \frac {1}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )} \, dx\\ &=\frac {2}{x}+32 \int \frac {x^2}{\left (4 x^2+36 \log (x)+7 x \log (x)\right )^2} \, dx+\frac {1544}{7} \int \frac {x}{\left (4 x^2+36 \log (x)+7 x \log (x)\right )^2} \, dx-288 \int \frac {1}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )} \, dx-\frac {27360}{49} \int \frac {1}{\left (4 x^2+36 \log (x)+7 x \log (x)\right )^2} \, dx+\frac {1492992}{49} \int \frac {1}{(36+7 x) \left (4 x^2+36 \log (x)+7 x \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 28, normalized size = 1.08 \begin {gather*} -2 \left (-\frac {1}{x}+\frac {4 x}{4 x^2+36 \log (x)+7 x \log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 29, normalized size = 1.12 \begin {gather*} \frac {2 \, {\left (7 \, x + 36\right )} \log \relax (x)}{4 \, x^{3} + {\left (7 \, x^{2} + 36 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.45, size = 26, normalized size = 1.00 \begin {gather*} -\frac {8 \, x}{4 \, x^{2} + 7 \, x \log \relax (x) + 36 \, \log \relax (x)} + \frac {2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 27, normalized size = 1.04
method | result | size |
risch | \(\frac {2}{x}-\frac {8 x}{7 x \ln \relax (x )+4 x^{2}+36 \ln \relax (x )}\) | \(27\) |
norman | \(\frac {14 x \ln \relax (x )+72 \ln \relax (x )}{x \left (7 x \ln \relax (x )+4 x^{2}+36 \ln \relax (x )\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 29, normalized size = 1.12 \begin {gather*} \frac {2 \, {\left (7 \, x + 36\right )} \log \relax (x)}{4 \, x^{3} + {\left (7 \, x^{2} + 36 \, x\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.40, size = 29, normalized size = 1.12 \begin {gather*} \frac {2\,\ln \relax (x)\,\left (7\,x+36\right )}{x\,\left (36\,\ln \relax (x)+7\,x\,\ln \relax (x)+4\,x^2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 19, normalized size = 0.73 \begin {gather*} - \frac {8 x}{4 x^{2} + \left (7 x + 36\right ) \log {\relax (x )}} + \frac {2}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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