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 = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.70, size = 27, normalized size = 0.82 \[ -\frac {15 \, B c x^{2} + 10 \, A b + 12 \, {\left (B b + A c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 27, normalized size = 0.82 \[ -\frac {15 \, B c x^{2} + 12 \, B b x + 12 \, A c x + 10 \, A b}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 0.85 \[ -\frac {B c}{4 x^{4}}-\frac {A b}{6 x^{6}}-\frac {A c +b B}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 27, normalized size = 0.82 \[ -\frac {15 \, B c x^{2} + 10 \, A b + 12 \, {\left (B b + A c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \[ -\frac {\frac {B\,c\,x^2}{4}+\left (\frac {A\,c}{5}+\frac {B\,b}{5}\right )\,x+\frac {A\,b}{6}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 31, normalized size = 0.94 \[ \frac {- 10 A b - 15 B c x^{2} + x \left (- 12 A c - 12 B b\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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