Optimal. Leaf size=33 \[ -\frac{A c+b B}{3 x^3}-\frac{A b}{4 x^4}-\frac{B c}{2 x^2} \]
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Rubi [A] time = 0.016918, 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} \[ -\frac{A c+b B}{3 x^3}-\frac{A b}{4 x^4}-\frac{B c}{2 x^2} \]
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^6} \, dx &=\int \left (\frac{A b}{x^5}+\frac{b B+A c}{x^4}+\frac{B c}{x^3}\right ) \, dx\\ &=-\frac{A b}{4 x^4}-\frac{b B+A c}{3 x^3}-\frac{B c}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0074544, size = 29, normalized size = 0.88 \[ -\frac{3 A b+4 A c x+4 b B x+6 B c x^2}{12 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Ab}{4\,{x}^{4}}}-{\frac{Bc}{2\,{x}^{2}}}-{\frac{Ac+bB}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.987884, size = 36, normalized size = 1.09 \begin{align*} -\frac{6 \, B c x^{2} + 3 \, A b + 4 \,{\left (B b + A c\right )} x}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83952, size = 66, normalized size = 2. \begin{align*} -\frac{6 \, B c x^{2} + 3 \, A b + 4 \,{\left (B b + A c\right )} x}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.555558, size = 31, normalized size = 0.94 \begin{align*} - \frac{3 A b + 6 B c x^{2} + x \left (4 A c + 4 B b\right )}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12281, size = 36, normalized size = 1.09 \begin{align*} -\frac{6 \, B c x^{2} + 4 \, B b x + 4 \, A c x + 3 \, A b}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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