Optimal. Leaf size=47 \[ -\frac{a B+A b}{5 x^5}-\frac{a A}{6 x^6}-\frac{A c+b B}{4 x^4}-\frac{B c}{3 x^3} \]
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Rubi [A] time = 0.0234613, 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} \[ -\frac{a B+A b}{5 x^5}-\frac{a A}{6 x^6}-\frac{A c+b B}{4 x^4}-\frac{B c}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a+b x+c x^2\right )}{x^7} \, dx &=\int \left (\frac{a A}{x^7}+\frac{A b+a B}{x^6}+\frac{b B+A c}{x^5}+\frac{B c}{x^4}\right ) \, dx\\ &=-\frac{a A}{6 x^6}-\frac{A b+a B}{5 x^5}-\frac{b B+A c}{4 x^4}-\frac{B c}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0153881, size = 45, normalized size = 0.96 \[ -\frac{2 a (5 A+6 B x)+x (3 A (4 b+5 c x)+5 B x (3 b+4 c x))}{60 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 40, normalized size = 0.9 \begin{align*} -{\frac{Bc}{3\,{x}^{3}}}-{\frac{Ab+aB}{5\,{x}^{5}}}-{\frac{Ac+bB}{4\,{x}^{4}}}-{\frac{aA}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08778, size = 53, normalized size = 1.13 \begin{align*} -\frac{20 \, B c x^{3} + 15 \,{\left (B b + A c\right )} x^{2} + 10 \, A a + 12 \,{\left (B a + A b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.21965, size = 99, normalized size = 2.11 \begin{align*} -\frac{20 \, B c x^{3} + 15 \,{\left (B b + A c\right )} x^{2} + 10 \, A a + 12 \,{\left (B a + A b\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.91403, size = 44, normalized size = 0.94 \begin{align*} - \frac{10 A a + 20 B c x^{3} + x^{2} \left (15 A c + 15 B b\right ) + x \left (12 A b + 12 B a\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.30237, size = 55, normalized size = 1.17 \begin{align*} -\frac{20 \, B c x^{3} + 15 \, B b x^{2} + 15 \, A c x^{2} + 12 \, B a x + 12 \, A b x + 10 \, A a}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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