Optimal. Leaf size=17 \[ 3-\frac {x (2+x) (x+\log (x))}{23+x} \]
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Rubi [A] time = 0.15, antiderivative size = 31, normalized size of antiderivative = 1.82, number of steps used = 14, number of rules used = 7, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.180, Rules used = {27, 6742, 43, 2357, 2295, 2314, 31} \begin {gather*} -x^2+21 x+\frac {11109}{x+23}+\frac {21 x \log (x)}{x+23}-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 31
Rule 43
Rule 2295
Rule 2314
Rule 2357
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-46-117 x-72 x^2-2 x^3+\left (-46-46 x-x^2\right ) \log (x)}{(23+x)^2} \, dx\\ &=\int \left (-\frac {46}{(23+x)^2}-\frac {117 x}{(23+x)^2}-\frac {72 x^2}{(23+x)^2}-\frac {2 x^3}{(23+x)^2}-\frac {\left (46+46 x+x^2\right ) \log (x)}{(23+x)^2}\right ) \, dx\\ &=\frac {46}{23+x}-2 \int \frac {x^3}{(23+x)^2} \, dx-72 \int \frac {x^2}{(23+x)^2} \, dx-117 \int \frac {x}{(23+x)^2} \, dx-\int \frac {\left (46+46 x+x^2\right ) \log (x)}{(23+x)^2} \, dx\\ &=\frac {46}{23+x}-2 \int \left (-46+x-\frac {12167}{(23+x)^2}+\frac {1587}{23+x}\right ) \, dx-72 \int \left (1+\frac {529}{(23+x)^2}-\frac {46}{23+x}\right ) \, dx-117 \int \left (-\frac {23}{(23+x)^2}+\frac {1}{23+x}\right ) \, dx-\int \left (\log (x)-\frac {483 \log (x)}{(23+x)^2}\right ) \, dx\\ &=20 x-x^2+\frac {11109}{23+x}+21 \log (23+x)+483 \int \frac {\log (x)}{(23+x)^2} \, dx-\int \log (x) \, dx\\ &=21 x-x^2+\frac {11109}{23+x}-x \log (x)+\frac {21 x \log (x)}{23+x}+21 \log (23+x)-21 \int \frac {1}{23+x} \, dx\\ &=21 x-x^2+\frac {11109}{23+x}-x \log (x)+\frac {21 x \log (x)}{23+x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 31, normalized size = 1.82 \begin {gather*} 21 x-x^2+\frac {483 (23-\log (x))}{23+x}+21 \log (x)-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 30, normalized size = 1.76 \begin {gather*} -\frac {x^{3} + 2 \, x^{2} + {\left (x^{2} + 2 \, x\right )} \log \relax (x) - 483 \, x - 11109}{x + 23} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 33, normalized size = 1.94 \begin {gather*} -x^{2} - {\left (x + \frac {483}{x + 23}\right )} \log \relax (x) + 21 \, x + \frac {11109}{x + 23} + 21 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.61, size = 30, normalized size = 1.76
method | result | size |
norman | \(\frac {-2 x^{2}-x^{3}-2 x \ln \relax (x )-x^{2} \ln \relax (x )}{x +23}\) | \(30\) |
default | \(-x^{2}+21 x +\frac {11109}{x +23}-x \ln \relax (x )+\frac {21 \ln \relax (x ) x}{x +23}\) | \(32\) |
risch | \(-\frac {\left (x^{2}+23 x +483\right ) \ln \relax (x )}{x +23}+\frac {-x^{3}+21 x \ln \relax (x )-2 x^{2}+483 \ln \relax (x )+483 x +11109}{x +23}\) | \(49\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.39, size = 54, normalized size = 3.18 \begin {gather*} -x^{2} + 20 \, x + \frac {x^{2} - {\left (x^{2} + 23 \, x + 529\right )} \log \relax (x) + 23 \, x}{x + 23} + \frac {46 \, \log \relax (x)}{x + 23} + \frac {11109}{x + 23} + 21 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.46, size = 15, normalized size = 0.88 \begin {gather*} -\frac {x\,\left (x+\ln \relax (x)\right )\,\left (x+2\right )}{x+23} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.18, size = 32, normalized size = 1.88 \begin {gather*} - x^{2} + 21 x + 21 \log {\relax (x )} + \frac {\left (- x^{2} - 23 x - 483\right ) \log {\relax (x )}}{x + 23} + \frac {11109}{x + 23} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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