Optimal. Leaf size=36 \[ -\frac {7}{3 (2-x)^3}+\frac {2}{(2-x)^2}+\frac {2}{2-x}+\log (2-x) \]
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Rubi [A]
time = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1864}
\begin {gather*} \frac {2}{2-x}+\frac {2}{(2-x)^2}-\frac {7}{3 (2-x)^3}+\log (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1864
Rubi steps
\begin {align*} \int \frac {1-4 x^2+x^3}{(-2+x)^4} \, dx &=\int \left (-\frac {7}{(-2+x)^4}-\frac {4}{(-2+x)^3}+\frac {2}{(-2+x)^2}+\frac {1}{-2+x}\right ) \, dx\\ &=-\frac {7}{3 (2-x)^3}+\frac {2}{(2-x)^2}+\frac {2}{2-x}+\log (2-x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 0.67 \begin {gather*} \frac {-29+30 x-6 x^2}{3 (-2+x)^3}+\log (-2+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 27, normalized size = 0.75
method | result | size |
norman | \(\frac {-2 x^{2}+10 x -\frac {29}{3}}{\left (-2+x \right )^{3}}+\ln \left (-2+x \right )\) | \(22\) |
risch | \(\frac {-2 x^{2}+10 x -\frac {29}{3}}{\left (-2+x \right )^{3}}+\ln \left (-2+x \right )\) | \(22\) |
default | \(\ln \left (-2+x \right )-\frac {2}{-2+x}+\frac {2}{\left (-2+x \right )^{2}}+\frac {7}{3 \left (-2+x \right )^{3}}\) | \(27\) |
meijerg | \(\frac {x \left (\frac {1}{4} x^{2}-\frac {3}{2} x +3\right )}{48 \left (1-\frac {x}{2}\right )^{3}}+\frac {x \left (\frac {11}{2} x^{2}-15 x +12\right )}{24 \left (1-\frac {x}{2}\right )^{3}}+\ln \left (1-\frac {x}{2}\right )-\frac {x^{3}}{12 \left (1-\frac {x}{2}\right )^{3}}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.15, size = 32, normalized size = 0.89 \begin {gather*} -\frac {6 \, x^{2} - 30 \, x + 29}{3 \, {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )}} + \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 46, normalized size = 1.28 \begin {gather*} -\frac {6 \, x^{2} - 3 \, {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} \log \left (x - 2\right ) - 30 \, x + 29}{3 \, {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 29, normalized size = 0.81 \begin {gather*} \frac {- 6 x^{2} + 30 x - 29}{3 x^{3} - 18 x^{2} + 36 x - 24} + \log {\left (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 = 23, normalized size = 0.64 \begin {gather*} -\frac {6 \, x^{2} - 30 \, x + 29}{3 \, {\left (x - 2\right )}^{3}} + \log \left ({\left | x - 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 22, normalized size = 0.61 \begin {gather*} \ln \left (x-2\right )-\frac {2\,x^2-10\,x+\frac {29}{3}}{{\left (x-2\right )}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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