Optimal. Leaf size=25 \[ \frac {12 \left (12+\frac {\log (2)}{5 (2+x) (3+2 x)}\right )}{x} \]
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Rubi [A] time = 0.09, antiderivative size = 36, normalized size of antiderivative = 1.44, number of steps used = 2, number of rules used = 1, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2074} \begin {gather*} \frac {6 \log (2)}{5 (x+2)}-\frac {16 \log (2)}{5 (2 x+3)}+\frac {720+\log (4)}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {6 \log (2)}{5 (2+x)^2}+\frac {32 \log (2)}{5 (3+2 x)^2}+\frac {-720-\log (4)}{5 x^2}\right ) \, dx\\ &=\frac {6 \log (2)}{5 (2+x)}-\frac {16 \log (2)}{5 (3+2 x)}+\frac {720+\log (4)}{5 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 31, normalized size = 1.24 \begin {gather*} \frac {4 \left (3240+3780 x+1080 x^2+\log (512)\right )}{15 x \left (6+7 x+2 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 30, normalized size = 1.20 \begin {gather*} \frac {12 \, {\left (120 \, x^{2} + 420 \, x + \log \relax (2) + 360\right )}}{5 \, {\left (2 \, x^{3} + 7 \, x^{2} + 6 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 30, normalized size = 1.20 \begin {gather*} \frac {12 \, {\left (120 \, x^{2} + 420 \, x + \log \relax (2) + 360\right )}}{5 \, {\left (2 \, x^{3} + 7 \, x^{2} + 6 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 30, normalized size = 1.20
method | result | size |
gosper | \(\frac {288 x^{2}+1008 x +864+\frac {12 \ln \relax (2)}{5}}{x \left (2 x^{2}+7 x +6\right )}\) | \(30\) |
norman | \(\frac {288 x^{2}+1008 x +864+\frac {12 \ln \relax (2)}{5}}{x \left (2 x^{2}+7 x +6\right )}\) | \(31\) |
risch | \(\frac {288 x^{2}+1008 x +864+\frac {12 \ln \relax (2)}{5}}{x \left (2 x^{2}+7 x +6\right )}\) | \(32\) |
default | \(-\frac {24 \left (-\frac {\ln \relax (2)}{12}-30\right )}{5 x}-\frac {16 \ln \relax (2)}{5 \left (2 x +3\right )}+\frac {6 \ln \relax (2)}{5 \left (2+x \right )}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 30, normalized size = 1.20 \begin {gather*} \frac {12 \, {\left (120 \, x^{2} + 420 \, x + \log \relax (2) + 360\right )}}{5 \, {\left (2 \, x^{3} + 7 \, x^{2} + 6 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 29, normalized size = 1.16 \begin {gather*} \frac {1440\,x^2+5040\,x+\ln \left (4096\right )+4320}{5\,\left (2\,x^3+7\,x^2+6\,x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.55, size = 31, normalized size = 1.24 \begin {gather*} - \frac {- 1440 x^{2} - 5040 x - 4320 - 12 \log {\relax (2 )}}{10 x^{3} + 35 x^{2} + 30 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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