Optimal. Leaf size=27 \[ \frac {x}{3 (-7+3 x-5 (3+x)+x (4-\log (4+x)))} \]
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Rubi [F]
time = 0.33, 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 {-88-22 x+x^2}{5808+396 x-216 x^2+12 x^3+\left (528 x+84 x^2-12 x^3\right ) \log (4+x)+\left (12 x^2+3 x^3\right ) \log ^2(4+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 {-88-22 x+x^2}{3 (4+x) (22-2 x+x \log (4+x))^2} \, dx\\ &=\frac {1}{3} \int \frac {-88-22 x+x^2}{(4+x) (22-2 x+x \log (4+x))^2} \, dx\\ &=\frac {1}{3} \int \left (-\frac {26}{(22-2 x+x \log (4+x))^2}+\frac {x}{(22-2 x+x \log (4+x))^2}+\frac {16}{(4+x) (22-2 x+x \log (4+x))^2}\right ) \, dx\\ &=\frac {1}{3} \int \frac {x}{(22-2 x+x \log (4+x))^2} \, dx+\frac {16}{3} \int \frac {1}{(4+x) (22-2 x+x \log (4+x))^2} \, dx-\frac {26}{3} \int \frac {1}{(22-2 x+x \log (4+x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 18, normalized size = 0.67 \begin {gather*} -\frac {x}{3 (22-2 x+x \log (4+x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.37, size = 25, normalized size = 0.93
method | result | size |
norman | \(-\frac {x}{3 \left (x \ln \left (4+x \right )-2 x +22\right )}\) | \(17\) |
risch | \(-\frac {x}{3 \left (x \ln \left (4+x \right )-2 x +22\right )}\) | \(17\) |
derivativedivides | \(-\frac {x}{3 \left (\left (4+x \right ) \ln \left (4+x \right )+22-2 x -4 \ln \left (4+x \right )\right )}\) | \(25\) |
default | \(-\frac {x}{3 \left (\left (4+x \right ) \ln \left (4+x \right )+22-2 x -4 \ln \left (4+x \right )\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 16, normalized size = 0.59 \begin {gather*} -\frac {x}{3 \, {\left (x \log \left (x + 4\right ) - 2 \, x + 22\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 0.59 \begin {gather*} -\frac {x}{3 \, {\left (x \log \left (x + 4\right ) - 2 \, x + 22\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 15, normalized size = 0.56 \begin {gather*} - \frac {x}{3 x \log {\left (x + 4 \right )} - 6 x + 66} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 0.59 \begin {gather*} -\frac {x}{3 \, {\left (x \log \left (x + 4\right ) - 2 \, x + 22\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.24, size = 17, normalized size = 0.63 \begin {gather*} -\frac {x}{3\,\left (x\,\ln \left (x+4\right )-2\,x+22\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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