Optimal. Leaf size=38 \[ -\frac{a^2 b}{x^3}-\frac{a^3}{6 x^6}+3 a b^2 \log (x)+\frac{b^3 x^3}{3} \]
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Rubi [A] time = 0.0183484, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{a^2 b}{x^3}-\frac{a^3}{6 x^6}+3 a b^2 \log (x)+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x^7} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^3} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (b^3+\frac{a^3}{x^3}+\frac{3 a^2 b}{x^2}+\frac{3 a b^2}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3}{6 x^6}-\frac{a^2 b}{x^3}+\frac{b^3 x^3}{3}+3 a b^2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0043317, size = 38, normalized size = 1. \[ -\frac{a^2 b}{x^3}-\frac{a^3}{6 x^6}+3 a b^2 \log (x)+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 35, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{6\,{x}^{6}}}-{\frac{{a}^{2}b}{{x}^{3}}}+{\frac{{b}^{3}{x}^{3}}{3}}+3\,a{b}^{2}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965134, size = 49, normalized size = 1.29 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + a b^{2} \log \left (x^{3}\right ) - \frac{6 \, a^{2} b x^{3} + a^{3}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59891, size = 85, normalized size = 2.24 \begin{align*} \frac{2 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} \log \left (x\right ) - 6 \, a^{2} b x^{3} - a^{3}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.521876, size = 36, normalized size = 0.95 \begin{align*} 3 a b^{2} \log{\left (x \right )} + \frac{b^{3} x^{3}}{3} - \frac{a^{3} + 6 a^{2} b x^{3}}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1117, size = 61, normalized size = 1.61 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + 3 \, a b^{2} \log \left ({\left | x \right |}\right ) - \frac{9 \, a b^{2} x^{6} + 6 \, a^{2} b x^{3} + a^{3}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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