Optimal. Leaf size=51 \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac{1}{3} b^2 B x^3 \]
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Rubi [A] time = 0.0375813, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {446, 76} \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac{1}{3} b^2 B x^3 \]
Antiderivative was successfully verified.
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Rule 446
Rule 76
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^7} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^2 (A+B x)}{x^3} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (b^2 B+\frac{a^2 A}{x^3}+\frac{a (2 A b+a B)}{x^2}+\frac{b (A b+2 a B)}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^2 A}{6 x^6}-\frac{a (2 A b+a B)}{3 x^3}+\frac{1}{3} b^2 B x^3+b (A b+2 a B) \log (x)\\ \end{align*}
Mathematica [A] time = 0.0193914, size = 51, normalized size = 1. \[ \frac{1}{6} \left (-\frac{a^2 \left (A+2 B x^3\right )}{x^6}+6 b \log (x) (2 a B+A b)-\frac{4 a A b}{x^3}+2 b^2 B x^3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 51, normalized size = 1. \begin{align*}{\frac{{b}^{2}B{x}^{3}}{3}}-{\frac{A{a}^{2}}{6\,{x}^{6}}}-{\frac{2\,abA}{3\,{x}^{3}}}-{\frac{{a}^{2}B}{3\,{x}^{3}}}+A\ln \left ( x \right ){b}^{2}+2\,B\ln \left ( x \right ) ab \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1939, size = 73, normalized size = 1.43 \begin{align*} \frac{1}{3} \, B b^{2} x^{3} + \frac{1}{3} \,{\left (2 \, B a b + A b^{2}\right )} \log \left (x^{3}\right ) - \frac{2 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.56835, size = 122, normalized size = 2.39 \begin{align*} \frac{2 \, B b^{2} x^{9} + 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} \log \left (x\right ) - 2 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - A a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.863031, size = 49, normalized size = 0.96 \begin{align*} \frac{B b^{2} x^{3}}{3} + b \left (A b + 2 B a\right ) \log{\left (x \right )} - \frac{A a^{2} + x^{3} \left (4 A a b + 2 B a^{2}\right )}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20273, size = 95, normalized size = 1.86 \begin{align*} \frac{1}{3} \, B b^{2} x^{3} +{\left (2 \, B a b + A b^{2}\right )} \log \left ({\left | x \right |}\right ) - \frac{6 \, B a b x^{6} + 3 \, A b^{2} x^{6} + 2 \, B a^{2} x^{3} + 4 \, A a b x^{3} + A a^{2}}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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