Optimal. Leaf size=33 \[ -\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4} \]
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Rubi [A] time = 0.0160021, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {765} \[ -\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (b x+c x^2\right )}{x^8} \, dx &=\int \left (\frac{A b}{x^7}+\frac{b B+A c}{x^6}+\frac{B c}{x^5}\right ) \, dx\\ &=-\frac{A b}{6 x^6}-\frac{b B+A c}{5 x^5}-\frac{B c}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.008755, size = 31, normalized size = 0.94 \[ -\frac{2 A (5 b+6 c x)+3 B x (4 b+5 c x)}{60 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Ac+bB}{5\,{x}^{5}}}-{\frac{Ab}{6\,{x}^{6}}}-{\frac{Bc}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03401, size = 36, normalized size = 1.09 \begin{align*} -\frac{15 \, B c x^{2} + 10 \, A b + 12 \,{\left (B b + A c\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68832, size = 70, normalized size = 2.12 \begin{align*} -\frac{15 \, B c x^{2} + 10 \, A b + 12 \,{\left (B b + A c\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.646628, size = 31, normalized size = 0.94 \begin{align*} - \frac{10 A b + 15 B c x^{2} + x \left (12 A c + 12 B b\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14288, size = 36, normalized size = 1.09 \begin{align*} -\frac{15 \, B c x^{2} + 12 \, B b x + 12 \, A c x + 10 \, A b}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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