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 = 0.0114004, antiderivative size = 37, 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} \[ -\frac{1}{6 (x+1)^6}+\frac{3}{7 (x+1)^7}-\frac{3}{8 (x+1)^8}+\frac{1}{9 (x+1)^9} \]
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*}
Mathematica [A] time = 0.0065565, 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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Maple [A] time = 0.005, size = 30, normalized size = 0.8 \begin{align*}{\frac{1}{9\, \left ( 1+x \right ) ^{9}}}-{\frac{3}{8\, \left ( 1+x \right ) ^{8}}}+{\frac{3}{7\, \left ( 1+x \right ) ^{7}}}-{\frac{1}{6\, \left ( 1+x \right ) ^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.944489, size = 84, normalized size = 2.27 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.03816, size = 157, normalized size = 4.24 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.139897, size = 61, normalized size = 1.65 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06152, size = 30, normalized size = 0.81 \begin{align*} -\frac{84 \, x^{3} + 36 \, x^{2} + 9 \, x + 1}{504 \,{\left (x + 1\right )}^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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