Optimal. Leaf size=24 \[ \frac {5 x}{4 \left (-x^3 (x+\log (x))+4 x \log (12+x)\right )} \]
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Rubi [A] time = 0.24, antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 3, number of rules used = 3, integrand size = 113, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {5}{4 \left (x^3+x^2 \log (x)-4 \log (x+12)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \left (-4+12 x+37 x^2+3 x^3+2 x (12+x) \log (x)\right )}{4 (12+x) \left (x^3+x^2 \log (x)-4 \log (12+x)\right )^2} \, dx\\ &=\frac {5}{4} \int \frac {-4+12 x+37 x^2+3 x^3+2 x (12+x) \log (x)}{(12+x) \left (x^3+x^2 \log (x)-4 \log (12+x)\right )^2} \, dx\\ &=-\frac {5}{4 \left (x^3+x^2 \log (x)-4 \log (12+x)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 22, normalized size = 0.92 \begin {gather*} -\frac {5}{4 \left (x^3+x^2 \log (x)-4 \log (12+x)\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 20, normalized size = 0.83 \begin {gather*} -\frac {5}{4 \, {\left (x^{3} + x^{2} \log \relax (x) - 4 \, \log \left (x + 12\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 20, normalized size = 0.83 \begin {gather*} -\frac {5}{4 \, {\left (x^{3} + x^{2} \log \relax (x) - 4 \, \log \left (x + 12\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.88
method | result | size |
risch | \(-\frac {5}{4 \left (x^{2} \ln \relax (x )+x^{3}-4 \ln \left (x +12\right )\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 20, normalized size = 0.83 \begin {gather*} -\frac {5}{4 \, {\left (x^{3} + x^{2} \log \relax (x) - 4 \, \log \left (x + 12\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {60\,x+\ln \relax (x)\,\left (10\,x^2+120\,x\right )+185\,x^2+15\,x^3-20}{\ln \relax (x)\,\left (8\,x^6+96\,x^5\right )+{\ln \left (x+12\right )}^2\,\left (64\,x+768\right )+{\ln \relax (x)}^2\,\left (4\,x^5+48\,x^4\right )-\ln \left (x+12\right )\,\left (\ln \relax (x)\,\left (32\,x^3+384\,x^2\right )+384\,x^3+32\,x^4\right )+48\,x^6+4\,x^7} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 20, normalized size = 0.83 \begin {gather*} \frac {5}{- 4 x^{3} - 4 x^{2} \log {\relax (x )} + 16 \log {\left (x + 12 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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