Optimal. Leaf size=37 \[ -\frac {1}{6 (x+1)^6}+\frac {3}{7 (x+1)^7}-\frac {3}{8 (x+1)^8}+\frac {1}{9 (x+1)^9} \]
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Rubi [A] time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, 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} \[ -\frac {1}{6 (x+1)^6}+\frac {3}{7 (x+1)^7}-\frac {3}{8 (x+1)^8}+\frac {1}{9 (x+1)^9} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {x^3}{(1+x)^{10}} \, dx &=\int \left (-\frac {1}{(1+x)^{10}}+\frac {3}{(1+x)^9}-\frac {3}{(1+x)^8}+\frac {1}{(1+x)^7}\right ) \, dx\\ &=\frac {1}{9 (1+x)^9}-\frac {3}{8 (1+x)^8}+\frac {3}{7 (1+x)^7}-\frac {1}{6 (1+x)^6}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 0.65 \[ -\frac {84 x^3+36 x^2+9 x+1}{504 (x+1)^9} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.39, size = 62, normalized size = 1.68 \[ -\frac {84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \, {\left (x^{9} + 9 \, x^{8} + 36 \, x^{7} + 84 \, x^{6} + 126 \, x^{5} + 126 \, x^{4} + 84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.87, size = 22, normalized size = 0.59 \[ -\frac {84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \, {\left (x + 1\right )}^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 30, normalized size = 0.81 \[ \frac {1}{9 \left (x +1\right )^{9}}-\frac {3}{8 \left (x +1\right )^{8}}+\frac {3}{7 \left (x +1\right )^{7}}-\frac {1}{6 \left (x +1\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.48, size = 62, normalized size = 1.68 \[ -\frac {84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \, {\left (x^{9} + 9 \, x^{8} + 36 \, x^{7} + 84 \, x^{6} + 126 \, x^{5} + 126 \, x^{4} + 84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 29, normalized size = 0.78 \[ \frac {3}{7\,{\left (x+1\right )}^7}-\frac {1}{6\,{\left (x+1\right )}^6}-\frac {3}{8\,{\left (x+1\right )}^8}+\frac {1}{9\,{\left (x+1\right )}^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 61, normalized size = 1.65 \[ \frac {- 84 x^{3} - 36 x^{2} - 9 x - 1}{504 x^{9} + 4536 x^{8} + 18144 x^{7} + 42336 x^{6} + 63504 x^{5} + 63504 x^{4} + 42336 x^{3} + 18144 x^{2} + 4536 x + 504} \]
Verification of antiderivative is not currently implemented for this CAS.
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