Optimal. Leaf size=19 \[ 1+x^3-\frac {4 x \log (2 x)}{3 (-5+x)} \]
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Rubi [A] time = 0.18, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps used = 14, number of rules used = 6, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {27, 12, 6742, 43, 2314, 31} \begin {gather*} x^3+\frac {4 x \log (2 x)}{3 (5-x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 31
Rule 43
Rule 2314
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20-4 x+225 x^2-90 x^3+9 x^4+20 \log (2 x)}{3 (-5+x)^2} \, dx\\ &=\frac {1}{3} \int \frac {20-4 x+225 x^2-90 x^3+9 x^4+20 \log (2 x)}{(-5+x)^2} \, dx\\ &=\frac {1}{3} \int \left (\frac {20}{(-5+x)^2}-\frac {4 x}{(-5+x)^2}+\frac {225 x^2}{(-5+x)^2}-\frac {90 x^3}{(-5+x)^2}+\frac {9 x^4}{(-5+x)^2}+\frac {20 \log (2 x)}{(-5+x)^2}\right ) \, dx\\ &=\frac {20}{3 (5-x)}-\frac {4}{3} \int \frac {x}{(-5+x)^2} \, dx+3 \int \frac {x^4}{(-5+x)^2} \, dx+\frac {20}{3} \int \frac {\log (2 x)}{(-5+x)^2} \, dx-30 \int \frac {x^3}{(-5+x)^2} \, dx+75 \int \frac {x^2}{(-5+x)^2} \, dx\\ &=\frac {20}{3 (5-x)}+\frac {4 x \log (2 x)}{3 (5-x)}-\frac {4}{3} \int \left (\frac {5}{(-5+x)^2}+\frac {1}{-5+x}\right ) \, dx+\frac {4}{3} \int \frac {1}{-5+x} \, dx+3 \int \left (75+\frac {625}{(-5+x)^2}+\frac {500}{-5+x}+10 x+x^2\right ) \, dx-30 \int \left (10+\frac {125}{(-5+x)^2}+\frac {75}{-5+x}+x\right ) \, dx+75 \int \left (1+\frac {25}{(-5+x)^2}+\frac {10}{-5+x}\right ) \, dx\\ &=x^3+\frac {4 x \log (2 x)}{3 (5-x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 27, normalized size = 1.42 \begin {gather*} \frac {1}{3} \left (3 x^3-4 \log (x)+\frac {20 \log (2 x)}{5-x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 25, normalized size = 1.32 \begin {gather*} \frac {3 \, x^{4} - 15 \, x^{3} - 4 \, x \log \left (2 \, x\right )}{3 \, {\left (x - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 19, normalized size = 1.00 \begin {gather*} x^{3} - \frac {20 \, \log \left (2 \, x\right )}{3 \, {\left (x - 5\right )}} - \frac {4}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.41, size = 19, normalized size = 1.00
method | result | size |
derivativedivides | \(x^{3}-\frac {8 \ln \left (2 x \right ) x}{3 \left (2 x -10\right )}\) | \(19\) |
default | \(x^{3}-\frac {8 \ln \left (2 x \right ) x}{3 \left (2 x -10\right )}\) | \(19\) |
risch | \(-\frac {20 \ln \left (2 x \right )}{3 \left (x -5\right )}+x^{3}-\frac {4 \ln \relax (x )}{3}\) | \(20\) |
norman | \(\frac {x^{4}-5 x^{3}-\frac {4 x \ln \left (2 x \right )}{3}}{x -5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 19, normalized size = 1.00 \begin {gather*} x^{3} - \frac {20 \, \log \left (2 \, x\right )}{3 \, {\left (x - 5\right )}} - \frac {4}{3} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.21, size = 27, normalized size = 1.42 \begin {gather*} -\frac {x\,\left (4\,\ln \left (2\,x\right )+15\,x^2-3\,x^3\right )}{3\,\left (x-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 20, normalized size = 1.05 \begin {gather*} x^{3} - \frac {4 \log {\relax (x )}}{3} - \frac {20 \log {\left (2 x \right )}}{3 x - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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