Optimal. Leaf size=47 \[ -\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4} \]
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Rubi [A] time = 0.0254179, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {765} \[ -\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a+b x+c x^2\right )}{x^8} \, dx &=\int \left (\frac{a A}{x^8}+\frac{A b+a B}{x^7}+\frac{b B+A c}{x^6}+\frac{B c}{x^5}\right ) \, dx\\ &=-\frac{a A}{7 x^7}-\frac{A b+a B}{6 x^6}-\frac{b B+A c}{5 x^5}-\frac{B c}{4 x^4}\\ \end{align*}
Mathematica [A] time = 0.017483, size = 46, normalized size = 0.98 \[ -\frac{10 a (6 A+7 B x)+7 x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))}{420 x^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 40, normalized size = 0.9 \begin{align*} -{\frac{aA}{7\,{x}^{7}}}-{\frac{Ac+bB}{5\,{x}^{5}}}-{\frac{Bc}{4\,{x}^{4}}}-{\frac{Ab+aB}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07298, size = 53, normalized size = 1.13 \begin{align*} -\frac{105 \, B c x^{3} + 84 \,{\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \,{\left (B a + A b\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.17057, size = 101, normalized size = 2.15 \begin{align*} -\frac{105 \, B c x^{3} + 84 \,{\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \,{\left (B a + A b\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 5.51216, size = 44, normalized size = 0.94 \begin{align*} - \frac{60 A a + 105 B c x^{3} + x^{2} \left (84 A c + 84 B b\right ) + x \left (70 A b + 70 B a\right )}{420 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24719, size = 55, normalized size = 1.17 \begin{align*} -\frac{105 \, B c x^{3} + 84 \, B b x^{2} + 84 \, A c x^{2} + 70 \, B a x + 70 \, A b x + 60 \, A a}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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