Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^4}{12 a x^{12}} \]
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Rubi [A] time = 0.0030226, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\left (a+b x^3\right )^4}{12 a x^{12}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x^{13}} \, dx &=-\frac{\left (a+b x^3\right )^4}{12 a x^{12}}\\ \end{align*}
Mathematica [B] time = 0.0036476, size = 43, normalized size = 2.26 \[ -\frac{a^2 b}{3 x^9}-\frac{a^3}{12 x^{12}}-\frac{a b^2}{2 x^6}-\frac{b^3}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 36, normalized size = 1.9 \begin{align*} -{\frac{{b}^{3}}{3\,{x}^{3}}}-{\frac{{a}^{3}}{12\,{x}^{12}}}-{\frac{a{b}^{2}}{2\,{x}^{6}}}-{\frac{{a}^{2}b}{3\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.99131, size = 47, normalized size = 2.47 \begin{align*} -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.63048, size = 78, normalized size = 4.11 \begin{align*} -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.611185, size = 37, normalized size = 1.95 \begin{align*} - \frac{a^{3} + 4 a^{2} b x^{3} + 6 a b^{2} x^{6} + 4 b^{3} x^{9}}{12 x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.12031, size = 47, normalized size = 2.47 \begin{align*} -\frac{4 \, b^{3} x^{9} + 6 \, a b^{2} x^{6} + 4 \, a^{2} b x^{3} + a^{3}}{12 \, x^{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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