Optimal. Leaf size=25 \[ \frac {4 (3-x) x (1+\log (2)) \log (-1+x)}{3-\frac {x}{25}} \]
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Rubi [A]
time = 0.33, antiderivative size = 45, normalized size of antiderivative = 1.80, number of steps
used = 14, number of rules used = 10, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {6820, 12,
6874, 147, 2465, 2436, 2332, 2442, 36, 31} \begin {gather*} 7300 (1+\log (2)) \log (1-x)-100 (1-x) (1+\log (2)) \log (x-1)-\frac {540000 (1+\log (2)) \log (x-1)}{75-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 31
Rule 36
Rule 147
Rule 2332
Rule 2436
Rule 2442
Rule 2465
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100 (1+\log (2)) \left (-x \left (225-78 x+x^2\right )-\left (-225+375 x-151 x^2+x^3\right ) \log (-1+x)\right )}{(1-x) (75-x)^2} \, dx\\ &=(100 (1+\log (2))) \int \frac {-x \left (225-78 x+x^2\right )-\left (-225+375 x-151 x^2+x^3\right ) \log (-1+x)}{(1-x) (75-x)^2} \, dx\\ &=(100 (1+\log (2))) \int \left (\frac {(-3+x) x}{(-75+x) (-1+x)}+\frac {\left (225-150 x+x^2\right ) \log (-1+x)}{(-75+x)^2}\right ) \, dx\\ &=(100 (1+\log (2))) \int \frac {(-3+x) x}{(-75+x) (-1+x)} \, dx+(100 (1+\log (2))) \int \frac {\left (225-150 x+x^2\right ) \log (-1+x)}{(-75+x)^2} \, dx\\ &=(100 (1+\log (2))) \int \left (1+\frac {2700}{37 (-75+x)}+\frac {1}{37 (-1+x)}\right ) \, dx+(100 (1+\log (2))) \int \left (\log (-1+x)-\frac {5400 \log (-1+x)}{(-75+x)^2}\right ) \, dx\\ &=100 x (1+\log (2))+\frac {100}{37} (1+\log (2)) \log (1-x)+\frac {270000}{37} (1+\log (2)) \log (75-x)+(100 (1+\log (2))) \int \log (-1+x) \, dx-(540000 (1+\log (2))) \int \frac {\log (-1+x)}{(-75+x)^2} \, dx\\ &=100 x (1+\log (2))+\frac {100}{37} (1+\log (2)) \log (1-x)+\frac {270000}{37} (1+\log (2)) \log (75-x)-\frac {540000 (1+\log (2)) \log (-1+x)}{75-x}+(100 (1+\log (2))) \text {Subst}(\int \log (x) \, dx,x,-1+x)-(540000 (1+\log (2))) \int \frac {1}{(-75+x) (-1+x)} \, dx\\ &=\frac {100}{37} (1+\log (2)) \log (1-x)+\frac {270000}{37} (1+\log (2)) \log (75-x)-100 (1-x) (1+\log (2)) \log (-1+x)-\frac {540000 (1+\log (2)) \log (-1+x)}{75-x}-\frac {1}{37} (270000 (1+\log (2))) \int \frac {1}{-75+x} \, dx+\frac {1}{37} (270000 (1+\log (2))) \int \frac {1}{-1+x} \, dx\\ &=7300 (1+\log (2)) \log (1-x)-100 (1-x) (1+\log (2)) \log (-1+x)-\frac {540000 (1+\log (2)) \log (-1+x)}{75-x}\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(53\) vs. \(2(25)=50\).
time = 0.06, size = 53, normalized size = 2.12 \begin {gather*} \frac {100}{37} (1+\log (2)) \left (5400 \tanh ^{-1}\left (\frac {1}{37} (-38+x)\right )+\log (1-x)+2700 \log (75-x)+\frac {199800 \log (-1+x)}{-75+x}+37 (-1+x) \log (-1+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs.
\(2(23)=46\).
time = 1.37, size = 66, normalized size = 2.64
method | result | size |
norman | \(\frac {\left (100+100 \ln \left (2\right )\right ) x^{2} \ln \left (x -1\right )+\left (-300-300 \ln \left (2\right )\right ) x \ln \left (x -1\right )}{x -75}\) | \(34\) |
risch | \(\frac {100 \left (x^{2} \ln \left (2\right )-75 x \ln \left (2\right )+x^{2}+5400 \ln \left (2\right )-75 x +5400\right ) \ln \left (x -1\right )}{x -75}+7200 \ln \left (2\right ) \ln \left (x -1\right )+7200 \ln \left (x -1\right )\) | \(50\) |
derivativedivides | \(100 \ln \left (2\right ) \ln \left (x -1\right ) \left (x -1\right )+\frac {270000 \ln \left (2\right ) \ln \left (x -1\right ) \left (x -1\right )}{37 \left (x -75\right )}+\frac {100 \ln \left (2\right ) \ln \left (x -1\right )}{37}+100 \left (x -1\right ) \ln \left (x -1\right )+\frac {270000 \ln \left (x -1\right ) \left (x -1\right )}{37 \left (x -75\right )}+\frac {100 \ln \left (x -1\right )}{37}\) | \(66\) |
default | \(100 \ln \left (2\right ) \ln \left (x -1\right ) \left (x -1\right )+\frac {270000 \ln \left (2\right ) \ln \left (x -1\right ) \left (x -1\right )}{37 \left (x -75\right )}+\frac {100 \ln \left (2\right ) \ln \left (x -1\right )}{37}+100 \left (x -1\right ) \ln \left (x -1\right )+\frac {270000 \ln \left (x -1\right ) \left (x -1\right )}{37 \left (x -75\right )}+\frac {100 \ln \left (x -1\right )}{37}\) | \(66\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 27, normalized size = 1.08 \begin {gather*} \frac {100 \, {\left (x^{2} {\left (\log \left (2\right ) + 1\right )} - 3 \, x {\left (\log \left (2\right ) + 1\right )}\right )} \log \left (x - 1\right )}{x - 75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 28, normalized size = 1.12 \begin {gather*} \frac {100 \, {\left (x^{2} + {\left (x^{2} - 3 \, x\right )} \log \left (2\right ) - 3 \, x\right )} \log \left (x - 1\right )}{x - 75} \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. 49 vs.
\(2 (20) = 40\).
time = 0.12, size = 49, normalized size = 1.96 \begin {gather*} \left (7200 \log {\left (2 \right )} + 7200\right ) \log {\left (x - 1 \right )} + \frac {\left (100 x^{2} \log {\left (2 \right )} + 100 x^{2} - 7500 x - 7500 x \log {\left (2 \right )} + 540000 \log {\left (2 \right )} + 540000\right ) \log {\left (x - 1 \right )}}{x - 75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 35, normalized size = 1.40 \begin {gather*} 100 \, {\left (x {\left (\log \left (2\right ) + 1\right )} + \frac {5400 \, {\left (\log \left (2\right ) + 1\right )}}{x - 75}\right )} \log \left (x - 1\right ) + 7200 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.45, size = 19, normalized size = 0.76 \begin {gather*} \frac {100\,x\,\ln \left (x-1\right )\,\left (\ln \left (2\right )+1\right )\,\left (x-3\right )}{x-75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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