Optimal. Leaf size=28 \[ 5 \log \left (e^4+x^2+\frac {1}{5} (x+\log (-1+x))-\log (3+2 x)\right ) \]
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Rubi [A] time = 0.26, antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 3, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {6688, 12, 6684} \begin {gather*} 5 \log \left (5 x^2+x+\log (x-1)-5 \log (2 x+3)+5 e^4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \left (-10+37 x-12 x^2-20 x^3\right )}{\left (3-x-2 x^2\right ) \left (5 e^4+x+5 x^2+\log (-1+x)-5 \log (3+2 x)\right )} \, dx\\ &=5 \int \frac {-10+37 x-12 x^2-20 x^3}{\left (3-x-2 x^2\right ) \left (5 e^4+x+5 x^2+\log (-1+x)-5 \log (3+2 x)\right )} \, dx\\ &=5 \log \left (5 e^4+x+5 x^2+\log (-1+x)-5 \log (3+2 x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.69, size = 27, normalized size = 0.96 \begin {gather*} 5 \log \left (5 e^4+x+5 x^2+\log (-1+x)-5 \log (3+2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 30, normalized size = 1.07 \begin {gather*} 5 \, \log \left (-5 \, x^{2} - x - 5 \, e^{4} + 5 \, \log \left (2 \, x + 3\right ) - \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 26, normalized size = 0.93 \begin {gather*} 5 \, \log \left (5 \, x^{2} + x + 5 \, e^{4} - 5 \, \log \left (2 \, x + 3\right ) + \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 29, normalized size = 1.04
method | result | size |
risch | \(5 \ln \left (\ln \left (2 x +3\right )-x^{2}-{\mathrm e}^{4}-\frac {x}{5}-\frac {\ln \left (x -1\right )}{5}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 28, normalized size = 1.00 \begin {gather*} 5 \, \log \left (-x^{2} - \frac {1}{5} \, x - e^{4} + \log \left (2 \, x + 3\right ) - \frac {1}{5} \, \log \left (x - 1\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.92, size = 26, normalized size = 0.93 \begin {gather*} 5\,\ln \left (\frac {x}{5}+\frac {\ln \left (x-1\right )}{5}+{\mathrm {e}}^4-\ln \left (2\,x+3\right )+x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.52, size = 26, normalized size = 0.93 \begin {gather*} 5 \log {\left (- x^{2} - \frac {x}{5} - \frac {\log {\left (x - 1 \right )}}{5} + \log {\left (2 x + 3 \right )} - e^{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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