Optimal. Leaf size=20 \[ 4-4 x^3 \log \left (\frac {25}{(2-x)^2 x^2}\right ) \]
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Rubi [A]
time = 0.16, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps
used = 10, number of rules used = 7, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.146, Rules used = {6820, 12,
6874, 78, 2581, 45, 30} \begin {gather*} -4 x^3 \log \left (\frac {25}{(2-x)^2 x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 45
Rule 78
Rule 2581
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 x^2 \left (4-4 x+3 (-2+x) \log \left (\frac {25}{(-2+x)^2 x^2}\right )\right )}{2-x} \, dx\\ &=4 \int \frac {x^2 \left (4-4 x+3 (-2+x) \log \left (\frac {25}{(-2+x)^2 x^2}\right )\right )}{2-x} \, dx\\ &=4 \int \left (\frac {4 (-1+x) x^2}{-2+x}-3 x^2 \log \left (\frac {25}{(-2+x)^2 x^2}\right )\right ) \, dx\\ &=-\left (12 \int x^2 \log \left (\frac {25}{(-2+x)^2 x^2}\right ) \, dx\right )+16 \int \frac {(-1+x) x^2}{-2+x} \, dx\\ &=-4 x^3 \log \left (\frac {25}{(2-x)^2 x^2}\right )-8 \int x^2 \, dx-8 \int \frac {x^3}{-2+x} \, dx+16 \int \left (2+\frac {4}{-2+x}+x+x^2\right ) \, dx\\ &=32 x+8 x^2+\frac {8 x^3}{3}+64 \log (2-x)-4 x^3 \log \left (\frac {25}{(2-x)^2 x^2}\right )-8 \int \left (4+\frac {8}{-2+x}+2 x+x^2\right ) \, dx\\ &=-4 x^3 \log \left (\frac {25}{(2-x)^2 x^2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 16, normalized size = 0.80 \begin {gather*} -4 x^3 \log \left (\frac {25}{(-2+x)^2 x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 29, normalized size = 1.45
method | result | size |
norman | \(-4 x^{3} \ln \left (\frac {25}{x^{4}-4 x^{3}+4 x^{2}}\right )\) | \(25\) |
risch | \(-4 x^{3} \ln \left (\frac {25}{x^{4}-4 x^{3}+4 x^{2}}\right )\) | \(25\) |
default | \(-8 x^{3} \ln \left (5\right )-4 x^{3} \ln \left (\frac {1}{x^{2} \left (x^{2}-4 x +4\right )}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 41 vs.
\(2 (18) = 36\).
time = 0.50, size = 41, normalized size = 2.05 \begin {gather*} -\frac {8}{3} \, x^{3} {\left (3 \, \log \left (5\right ) + 2\right )} + 8 \, x^{3} \log \left (x\right ) + \frac {16}{3} \, x^{3} + 8 \, {\left (x^{3} - 8\right )} \log \left (x - 2\right ) + 64 \, \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 24, normalized size = 1.20 \begin {gather*} -4 \, x^{3} \log \left (\frac {25}{x^{4} - 4 \, x^{3} + 4 \, x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 1.10 \begin {gather*} - 4 x^{3} \log {\left (\frac {25}{x^{4} - 4 x^{3} + 4 x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 24, normalized size = 1.20 \begin {gather*} -4 \, x^{3} \log \left (\frac {25}{x^{4} - 4 \, x^{3} + 4 \, x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.73, size = 27, normalized size = 1.35 \begin {gather*} -4\,x^3\,\left (2\,\ln \left (5\right )+\ln \left (\frac {1}{x^4-4\,x^3+4\,x^2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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