Optimal. Leaf size=33 \[ -\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3} \]
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Rubi [A] time = 0.0166344, 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} \[ -\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3} \]
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^7} \, dx &=\int \left (\frac{A b}{x^6}+\frac{b B+A c}{x^5}+\frac{B c}{x^4}\right ) \, dx\\ &=-\frac{A b}{5 x^5}-\frac{b B+A c}{4 x^4}-\frac{B c}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0098749, size = 31, normalized size = 0.94 \[ -\frac{3 A (4 b+5 c x)+5 B x (3 b+4 c x)}{60 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \begin{align*} -{\frac{Ac+bB}{4\,{x}^{4}}}-{\frac{Ab}{5\,{x}^{5}}}-{\frac{Bc}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986634, size = 36, normalized size = 1.09 \begin{align*} -\frac{20 \, B c x^{2} + 12 \, A b + 15 \,{\left (B b + A c\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87164, size = 70, normalized size = 2.12 \begin{align*} -\frac{20 \, B c x^{2} + 12 \, A b + 15 \,{\left (B b + A c\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.566476, size = 31, normalized size = 0.94 \begin{align*} - \frac{12 A b + 20 B c x^{2} + x \left (15 A c + 15 B b\right )}{60 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13647, size = 36, normalized size = 1.09 \begin{align*} -\frac{20 \, B c x^{2} + 15 \, B b x + 15 \, A c x + 12 \, A b}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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