Optimal. Leaf size=29 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{6 x^6}+b B \log (x) \]
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Rubi [A] time = 0.0211706, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {446, 76} \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{6 x^6}+b B \log (x) \]
Antiderivative was successfully verified.
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Rule 446
Rule 76
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^7} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x) (A+B x)}{x^3} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a A}{x^3}+\frac{A b+a B}{x^2}+\frac{b B}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac{a A}{6 x^6}-\frac{A b+a B}{3 x^3}+b B \log (x)\\ \end{align*}
Mathematica [A] time = 0.016098, size = 31, normalized size = 1.07 \[ \frac{-a B-A b}{3 x^3}-\frac{a A}{6 x^6}+b B \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 1. \begin{align*} -{\frac{Ab}{3\,{x}^{3}}}-{\frac{Ba}{3\,{x}^{3}}}-{\frac{Aa}{6\,{x}^{6}}}+bB\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.33586, size = 41, normalized size = 1.41 \begin{align*} \frac{1}{3} \, B b \log \left (x^{3}\right ) - \frac{2 \,{\left (B a + A b\right )} x^{3} + A a}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47408, size = 73, normalized size = 2.52 \begin{align*} \frac{6 \, B b x^{6} \log \left (x\right ) - 2 \,{\left (B a + A b\right )} x^{3} - A a}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.65047, size = 27, normalized size = 0.93 \begin{align*} B b \log{\left (x \right )} - \frac{A a + x^{3} \left (2 A b + 2 B a\right )}{6 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19674, size = 50, normalized size = 1.72 \begin{align*} B b \log \left ({\left | x \right |}\right ) - \frac{3 \, B b x^{6} + 2 \, B a x^{3} + 2 \, A b x^{3} + A a}{6 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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