Optimal. Leaf size=23 \[ \frac {3 x}{4+\frac {1}{4} \log \left (\frac {2}{(-1+x)^2}\right )-\log (x)} \]
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Rubi [F]
time = 0.51, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 \left (20-22 x-(-1+x) \log \left (\frac {2}{(-1+x)^2}\right )+4 (-1+x) \log (x)\right )}{(1-x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx\\ &=12 \int \frac {20-22 x-(-1+x) \log \left (\frac {2}{(-1+x)^2}\right )+4 (-1+x) \log (x)}{(1-x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx\\ &=12 \int \left (\frac {2 (-2+3 x)}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}+\frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)}\right ) \, dx\\ &=12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \frac {-2+3 x}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx\\ &=12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \left (\frac {3}{\left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}+\frac {1}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}\right ) \, dx\\ &=12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \frac {1}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx+72 \int \frac {1}{\left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 19, normalized size = 0.83 \begin {gather*} \frac {12 x}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 33.06, size = 81, normalized size = 3.52
method | result | size |
default | \(-\frac {24 i x}{\pi \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )-2 \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )^{2}+\pi \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )^{3}-2 i \ln \left (2\right )+8 i \ln \left (x \right )+4 i \ln \left (x -1\right )-32 i}\) | \(81\) |
risch | \(-\frac {24 i x}{\pi \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )-2 \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )^{2}+\pi \mathrm {csgn}\left (i \left (x -1\right )^{2}\right )^{3}-2 i \ln \left (2\right )+8 i \ln \left (x \right )+4 i \ln \left (x -1\right )-32 i}\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 19, normalized size = 0.83 \begin {gather*} \frac {12 \, x}{\log \left (2\right ) - 2 \, \log \left (x - 1\right ) - 4 \, \log \left (x\right ) + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 26, normalized size = 1.13 \begin {gather*} -\frac {12 \, x}{4 \, \log \left (x\right ) - \log \left (\frac {2}{x^{2} - 2 \, x + 1}\right ) - 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 20, normalized size = 0.87 \begin {gather*} \frac {12 x}{- 4 \log {\left (x \right )} + \log {\left (\frac {2}{x^{2} - 2 x + 1} \right )} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 24, normalized size = 1.04 \begin {gather*} \frac {12 \, x}{\log \left (2\right ) - \log \left (x^{2} - 2 \, x + 1\right ) - 4 \, \log \left (x\right ) + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {264\,x-\ln \left (x\right )\,\left (48\,x-48\right )+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (12\,x-12\right )-240}{256\,x-\ln \left (x\right )\,\left (128\,x+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (8\,x-8\right )-128\right )+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (32\,x-32\right )+{\ln \left (\frac {2}{x^2-2\,x+1}\right )}^2\,\left (x-1\right )+{\ln \left (x\right )}^2\,\left (16\,x-16\right )-256} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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