Optimal. Leaf size=23 \[ (1+x) \left (-x+(5-x)^4 x^2-\log (x)\right ) \]
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Rubi [A]
time = 0.13, 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 = {1607, 6820,
2332} \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 1607
Rule 2332
Rule 6820
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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Maple [A]
time = 1.21, size = 42, normalized size = 1.83
method | result | size |
default | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \left (x \right )+624 x^{2}-\ln \left (x \right )\) | \(42\) |
norman | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \left (x \right )+624 x^{2}-\ln \left (x \right )\) | \(42\) |
risch | \(x^{7}-19 x^{6}+130 x^{5}-350 x^{4}+125 x^{3}-x -x \ln \left (x \right )+624 x^{2}-\ln \left (x \right )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, 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 \left (x\right ) - x - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, 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 \left (x\right ) - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 37 vs.
\(2 (15) = 30\).
time = 0.07, 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 {\left (x \right )} - x - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, 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 \left (x\right ) - x - \log \left (x\right ) \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 \left (x\right )-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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