Optimal. Leaf size=47 \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{A c+b B}{3 x^3}-\frac{B c}{2 x^2} \]
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Rubi [A] time = 0.0243442, 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} \[ -\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{A c+b B}{3 x^3}-\frac{B c}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a+b x+c x^2\right )}{x^6} \, dx &=\int \left (\frac{a A}{x^6}+\frac{A b+a B}{x^5}+\frac{b B+A c}{x^4}+\frac{B c}{x^3}\right ) \, dx\\ &=-\frac{a A}{5 x^5}-\frac{A b+a B}{4 x^4}-\frac{b B+A c}{3 x^3}-\frac{B c}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0152054, size = 44, normalized size = 0.94 \[ -\frac{3 a (4 A+5 B x)+5 x \left (3 A b+4 A c x+4 b B x+6 B c x^2\right )}{60 x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 40, normalized size = 0.9 \begin{align*} -{\frac{Ac+bB}{3\,{x}^{3}}}-{\frac{Bc}{2\,{x}^{2}}}-{\frac{aA}{5\,{x}^{5}}}-{\frac{Ab+aB}{4\,{x}^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99919, size = 53, normalized size = 1.13 \begin{align*} -\frac{30 \, B c x^{3} + 20 \,{\left (B b + A c\right )} x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.13698, size = 99, normalized size = 2.11 \begin{align*} -\frac{30 \, B c x^{3} + 20 \,{\left (B b + A c\right )} x^{2} + 12 \, A a + 15 \,{\left (B a + A b\right )} x}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.4854, size = 44, normalized size = 0.94 \begin{align*} - \frac{12 A a + 30 B c x^{3} + x^{2} \left (20 A c + 20 B b\right ) + x \left (15 A b + 15 B a\right )}{60 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.37833, size = 55, normalized size = 1.17 \begin{align*} -\frac{30 \, B c x^{3} + 20 \, B b x^{2} + 20 \, A c x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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