Optimal. Leaf size=14 \[ -\frac{1}{5 b (a+b x)^5} \]
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Rubi [A] time = 0.0086401, 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} \[ -\frac{1}{5 b (a+b x)^5} \]
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 )^2} \, dx &=\int \frac{1}{(a+b x)^6} \, dx\\ &=-\frac{1}{5 b (a+b x)^5}\\ \end{align*}
Mathematica [A] time = 0.0034624, size = 14, normalized size = 1. \[ -\frac{1}{5 b (a+b x)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.9 \begin{align*} -{\frac{1}{5\,b \left ( bx+a \right ) ^{5}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.19541, size = 77, normalized size = 5.5 \begin{align*} -\frac{1}{5 \,{\left (b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.18818, size = 116, normalized size = 8.29 \begin{align*} -\frac{1}{5 \,{\left (b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.494435, size = 61, normalized size = 4.36 \begin{align*} - \frac{1}{5 a^{5} b + 25 a^{4} b^{2} x + 50 a^{3} b^{3} x^{2} + 50 a^{2} b^{4} x^{3} + 25 a b^{5} x^{4} + 5 b^{6} x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08833, size = 16, normalized size = 1.14 \begin{align*} -\frac{1}{5 \,{\left (b x + a\right )}^{5} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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