Optimal. Leaf size=21 \[ \frac {-\frac {21}{2}+\frac {x^2}{(1-x)^2}+\log (9)}{x^2} \]
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Rubi [A]
time = 0.04, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps
used = 2, number of rules used = 1, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2099}
\begin {gather*} \frac {1}{(x-1)^2}-\frac {21-\log (81)}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2}{(-1+x)^3}+\frac {21-2 \log (9)}{x^3}\right ) \, dx\\ &=\frac {1}{(-1+x)^2}-\frac {21-\log (81)}{2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 31, normalized size = 1.48 \begin {gather*} \frac {-21+x^2 (-19+\log (81))+\log (81)-x (-42+\log (6561))}{2 (-1+x)^2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 18, normalized size = 0.86
method | result | size |
default | \(-\frac {-4 \ln \left (3\right )+21}{2 x^{2}}+\frac {1}{\left (x -1\right )^{2}}\) | \(18\) |
norman | \(\frac {\left (-4 \ln \left (3\right )+21\right ) x +\left (2 \ln \left (3\right )-\frac {19}{2}\right ) x^{2}-\frac {21}{2}+2 \ln \left (3\right )}{x^{2} \left (x -1\right )^{2}}\) | \(34\) |
risch | \(\frac {\left (-4 \ln \left (3\right )+21\right ) x +\left (2 \ln \left (3\right )-\frac {19}{2}\right ) x^{2}-\frac {21}{2}+2 \ln \left (3\right )}{x^{2} \left (x^{2}-2 x +1\right )}\) | \(39\) |
gosper | \(\frac {4 x^{2} \ln \left (3\right )-8 x \ln \left (3\right )-19 x^{2}+4 \ln \left (3\right )+42 x -21}{2 x^{2} \left (x^{2}-2 x +1\right )}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 41, normalized size = 1.95 \begin {gather*} \frac {x^{2} {\left (4 \, \log \left (3\right ) - 19\right )} - 2 \, x {\left (4 \, \log \left (3\right ) - 21\right )} + 4 \, \log \left (3\right ) - 21}{2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 38, normalized size = 1.81 \begin {gather*} -\frac {19 \, x^{2} - 4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (3\right ) - 42 \, x + 21}{2 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )}} \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. 39 vs.
\(2 (19) = 38\).
time = 0.39, size = 39, normalized size = 1.86 \begin {gather*} \frac {x^{2} \left (-19 + 4 \log {\left (3 \right )}\right ) + x \left (42 - 8 \log {\left (3 \right )}\right ) - 21 + 4 \log {\left (3 \right )}}{2 x^{4} - 4 x^{3} + 2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 37, normalized size = 1.76 \begin {gather*} \frac {4 \, x^{2} \log \left (3\right ) - 19 \, x^{2} - 8 \, x \log \left (3\right ) + 42 \, x + 4 \, \log \left (3\right ) - 21}{2 \, {\left (x^{2} - x\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.81, size = 101, normalized size = 4.81 \begin {gather*} \mathrm {atanh}\left (\frac {2\,\left (2\,x-1\right )\,\left (24\,\ln \left (3\right )-6\,\ln \left (81\right )\right )}{48\,\ln \left (3\right )-12\,\ln \left (81\right )}\right )\,\left (48\,\ln \left (3\right )-12\,\ln \left (81\right )\right )-\frac {\left (24\,\ln \left (3\right )-6\,\ln \left (81\right )\right )\,x^3+\left (\frac {17\,\ln \left (81\right )}{2}-36\,\ln \left (3\right )+\frac {19}{2}\right )\,x^2+\left (12\,\ln \left (3\right )-2\,\ln \left (81\right )-21\right )\,x-\frac {\ln \left (81\right )}{2}+\frac {21}{2}}{x^4-2\,x^3+x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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