Optimal. Leaf size=45 \[ -\frac{1}{8 (1-x)^8}+\frac{1}{3 (1-x)^9}-\frac{3}{10 (1-x)^{10}}+\frac{1}{11 (1-x)^{11}} \]
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Rubi [A] time = 0.0124213, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ -\frac{1}{8 (1-x)^8}+\frac{1}{3 (1-x)^9}-\frac{3}{10 (1-x)^{10}}+\frac{1}{11 (1-x)^{11}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x^3}{(-1+x)^{12}} \, dx &=\int \left (\frac{1}{(-1+x)^{12}}+\frac{3}{(-1+x)^{11}}+\frac{3}{(-1+x)^{10}}+\frac{1}{(-1+x)^9}\right ) \, dx\\ &=\frac{1}{11 (1-x)^{11}}-\frac{3}{10 (1-x)^{10}}+\frac{1}{3 (1-x)^9}-\frac{1}{8 (1-x)^8}\\ \end{align*}
Mathematica [A] time = 0.0063717, size = 24, normalized size = 0.53 \[ \frac{-165 x^3+55 x^2-11 x+1}{1320 (x-1)^{11}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 30, normalized size = 0.7 \begin{align*} -{\frac{3}{10\, \left ( -1+x \right ) ^{10}}}-{\frac{1}{11\, \left ( -1+x \right ) ^{11}}}-{\frac{1}{8\, \left ( -1+x \right ) ^{8}}}-{\frac{1}{3\, \left ( -1+x \right ) ^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.936681, size = 97, normalized size = 2.16 \begin{align*} -\frac{165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1}{1320 \,{\left (x^{11} - 11 \, x^{10} + 55 \, x^{9} - 165 \, x^{8} + 330 \, x^{7} - 462 \, x^{6} + 462 \, x^{5} - 330 \, x^{4} + 165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.89486, size = 196, normalized size = 4.36 \begin{align*} -\frac{165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1}{1320 \,{\left (x^{11} - 11 \, x^{10} + 55 \, x^{9} - 165 \, x^{8} + 330 \, x^{7} - 462 \, x^{6} + 462 \, x^{5} - 330 \, x^{4} + 165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.161188, size = 71, normalized size = 1.58 \begin{align*} - \frac{165 x^{3} - 55 x^{2} + 11 x - 1}{1320 x^{11} - 14520 x^{10} + 72600 x^{9} - 217800 x^{8} + 435600 x^{7} - 609840 x^{6} + 609840 x^{5} - 435600 x^{4} + 217800 x^{3} - 72600 x^{2} + 14520 x - 1320} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05528, size = 30, normalized size = 0.67 \begin{align*} -\frac{165 \, x^{3} - 55 \, x^{2} + 11 \, x - 1}{1320 \,{\left (x - 1\right )}^{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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