Optimal. Leaf size=37 \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{9 x^9}-\frac{a b^2}{x^3}+b^3 \log (x) \]
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Rubi [A] time = 0.017969, antiderivative size = 37, 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} \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{9 x^9}-\frac{a b^2}{x^3}+b^3 \log (x) \]
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^{10}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^4} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^3}{x^4}+\frac{3 a^2 b}{x^3}+\frac{3 a b^2}{x^2}+\frac{b^3}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3}{9 x^9}-\frac{a^2 b}{2 x^6}-\frac{a b^2}{x^3}+b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0042846, size = 37, normalized size = 1. \[ -\frac{a^2 b}{2 x^6}-\frac{a^3}{9 x^9}-\frac{a b^2}{x^3}+b^3 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 34, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{9\,{x}^{9}}}-{\frac{{a}^{2}b}{2\,{x}^{6}}}-{\frac{a{b}^{2}}{{x}^{3}}}+{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958666, size = 53, normalized size = 1.43 \begin{align*} \frac{1}{3} \, b^{3} \log \left (x^{3}\right ) - \frac{18 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66096, size = 90, normalized size = 2.43 \begin{align*} \frac{18 \, b^{3} x^{9} \log \left (x\right ) - 18 \, a b^{2} x^{6} - 9 \, a^{2} b x^{3} - 2 \, a^{3}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.561111, size = 36, normalized size = 0.97 \begin{align*} b^{3} \log{\left (x \right )} - \frac{2 a^{3} + 9 a^{2} b x^{3} + 18 a b^{2} x^{6}}{18 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10043, size = 61, normalized size = 1.65 \begin{align*} b^{3} \log \left ({\left | x \right |}\right ) - \frac{11 \, b^{3} x^{9} + 18 \, a b^{2} x^{6} + 9 \, a^{2} b x^{3} + 2 \, a^{3}}{18 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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