Optimal. Leaf size=30 \[ -x+\log \left (-\left ((3+x) \left (1+\left (3 x-x^2\right )^2\right )\right )+\log (1+2 x)\right ) \]
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Rubi [A] time = 0.77, antiderivative size = 34, normalized size of antiderivative = 1.13, number of steps used = 4, number of rules used = 3, integrand size = 87, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6741, 6742, 6684} \begin {gather*} \log \left (x^5-3 x^4-9 x^3+27 x^2+x-\log (2 x+1)+3\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4+49 x+52 x^2-111 x^3+2 x^4+15 x^5-2 x^6-(-1-2 x) \log (1+2 x)}{(1+2 x) \left (3+x+27 x^2-9 x^3-3 x^4+x^5-\log (1+2 x)\right )} \, dx\\ &=\int \left (-1+\frac {-1+56 x+81 x^2-66 x^3-19 x^4+10 x^5}{(1+2 x) \left (3+x+27 x^2-9 x^3-3 x^4+x^5-\log (1+2 x)\right )}\right ) \, dx\\ &=-x+\int \frac {-1+56 x+81 x^2-66 x^3-19 x^4+10 x^5}{(1+2 x) \left (3+x+27 x^2-9 x^3-3 x^4+x^5-\log (1+2 x)\right )} \, dx\\ &=-x+\log \left (3+x+27 x^2-9 x^3-3 x^4+x^5-\log (1+2 x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 56, normalized size = 1.87 \begin {gather*} -x+\log \left (325-495 (1+2 x)+278 (1+2 x)^2-2 (1+2 x)^3-11 (1+2 x)^4+(1+2 x)^5-32 \log (1+2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 36, normalized size = 1.20 \begin {gather*} -x + \log \left (-x^{5} + 3 \, x^{4} + 9 \, x^{3} - 27 \, x^{2} - x + \log \left (2 \, x + 1\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 34, normalized size = 1.13 \begin {gather*} -x + \log \left (x^{5} - 3 \, x^{4} - 9 \, x^{3} + 27 \, x^{2} + x - \log \left (2 \, x + 1\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 35, normalized size = 1.17
method | result | size |
norman | \(-x +\ln \left (x^{5}-3 x^{4}-9 x^{3}+27 x^{2}+x -\ln \left (2 x +1\right )+3\right )\) | \(35\) |
risch | \(-x +\ln \left (-x^{5}+3 x^{4}+9 x^{3}-27 x^{2}-x +\ln \left (2 x +1\right )-3\right )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 36, normalized size = 1.20 \begin {gather*} -x + \log \left (-x^{5} + 3 \, x^{4} + 9 \, x^{3} - 27 \, x^{2} - x + \log \left (2 \, x + 1\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 34, normalized size = 1.13 \begin {gather*} \ln \left (x-\ln \left (2\,x+1\right )+27\,x^2-9\,x^3-3\,x^4+x^5+3\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 31, normalized size = 1.03 \begin {gather*} - x + \log {\left (- x^{5} + 3 x^{4} + 9 x^{3} - 27 x^{2} - x + \log {\left (2 x + 1 \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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