Optimal. Leaf size=14 \[ -\frac{1}{8 b (a+b x)^8} \]
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Rubi [A] time = 0.0081347, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069, Rules used = {2058, 32} \[ -\frac{1}{8 b (a+b x)^8} \]
Antiderivative was successfully verified.
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Rule 2058
Rule 32
Rubi steps
\begin{align*} \int \frac{1}{\left (a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3\right )^3} \, dx &=\int \frac{1}{(a+b x)^9} \, dx\\ &=-\frac{1}{8 b (a+b x)^8}\\ \end{align*}
Mathematica [A] time = 0.0029336, size = 14, normalized size = 1. \[ -\frac{1}{8 b (a+b x)^8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{8\,b \left ( bx+a \right ) ^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.13839, size = 122, normalized size = 8.71 \begin{align*} -\frac{1}{8 \,{\left (b^{9} x^{8} + 8 \, a b^{8} x^{7} + 28 \, a^{2} b^{7} x^{6} + 56 \, a^{3} b^{6} x^{5} + 70 \, a^{4} b^{5} x^{4} + 56 \, a^{5} b^{4} x^{3} + 28 \, a^{6} b^{3} x^{2} + 8 \, a^{7} b^{2} x + a^{8} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.21306, size = 185, normalized size = 13.21 \begin{align*} -\frac{1}{8 \,{\left (b^{9} x^{8} + 8 \, a b^{8} x^{7} + 28 \, a^{2} b^{7} x^{6} + 56 \, a^{3} b^{6} x^{5} + 70 \, a^{4} b^{5} x^{4} + 56 \, a^{5} b^{4} x^{3} + 28 \, a^{6} b^{3} x^{2} + 8 \, a^{7} b^{2} x + a^{8} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.73029, size = 97, normalized size = 6.93 \begin{align*} - \frac{1}{8 a^{8} b + 64 a^{7} b^{2} x + 224 a^{6} b^{3} x^{2} + 448 a^{5} b^{4} x^{3} + 560 a^{4} b^{5} x^{4} + 448 a^{3} b^{6} x^{5} + 224 a^{2} b^{7} x^{6} + 64 a b^{8} x^{7} + 8 b^{9} x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07468, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{8 \,{\left (b x + a\right )}^{8} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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