Optimal. Leaf size=23 \[ (1+x) \left (-x+(5-x)^4 x^2-\log (x)\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 41, normalized size of antiderivative = 1.78, number of steps used = 4, number of rules used = 3, integrand size = 61, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {1593, 6688, 2295} \begin {gather*} x^7-19 x^6+130 x^5-350 x^4+125 x^3+624 x^2-x-x \log (x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 2295
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5+9 x+8 x^2-2 x^3+(5-x)^4 \left (-10 x^2-9 x^3+7 x^4\right )+\left (5 x-x^2\right ) \log (x)}{(-5+x) x} \, dx\\ &=\int \left (-2-\frac {1}{x}+1248 x+375 x^2-1400 x^3+650 x^4-114 x^5+7 x^6-\log (x)\right ) \, dx\\ &=-2 x+624 x^2+125 x^3-350 x^4+130 x^5-19 x^6+x^7-\log (x)-\int \log (x) \, dx\\ &=-x+624 x^2+125 x^3-350 x^4+130 x^5-19 x^6+x^7-\log (x)-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 41, normalized size = 1.78 \begin {gather*} -x+624 x^2+125 x^3-350 x^4+130 x^5-19 x^6+x^7-\log (x)-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 39, normalized size = 1.70 \begin {gather*} x^{7} - 19 \, x^{6} + 130 \, x^{5} - 350 \, x^{4} + 125 \, x^{3} + 624 \, x^{2} - {\left (x + 1\right )} \log \relax (x) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 41, normalized size = 1.78 \begin {gather*} x^{7} - 19 \, x^{6} + 130 \, x^{5} - 350 \, x^{4} + 125 \, x^{3} + 624 \, x^{2} - x \log \relax (x) - x - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.33, size = 42, normalized size = 1.83
method | result | size |
default | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \relax (x )+624 x^{2}-\ln \relax (x )\) | \(42\) |
norman | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \relax (x )+624 x^{2}-\ln \relax (x )\) | \(42\) |
risch | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \relax (x )+624 x^{2}-\ln \relax (x )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 41, normalized size = 1.78 \begin {gather*} x^{7} - 19 \, x^{6} + 130 \, x^{5} - 350 \, x^{4} + 125 \, x^{3} + 624 \, x^{2} - x \log \relax (x) - x - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.49, size = 34, normalized size = 1.48 \begin {gather*} -\left (x+1\right )\,\left (x+\ln \relax (x)-625\,x^2+500\,x^3-150\,x^4+20\,x^5-x^6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 37, normalized size = 1.61 \begin {gather*} x^{7} - 19 x^{6} + 130 x^{5} - 350 x^{4} + 125 x^{3} + 624 x^{2} - x \log {\relax (x )} - x - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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