Optimal. Leaf size=75 \[ -\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{4 x^4}-\frac{B c^3}{2 x^2} \]
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Rubi [A] time = 0.0374368, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {765} \[ -\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{4 x^4}-\frac{B c^3}{2 x^2} \]
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 )^3}{x^{10}} \, dx &=\int \left (\frac{A b^3}{x^7}+\frac{b^2 (b B+3 A c)}{x^6}+\frac{3 b c (b B+A c)}{x^5}+\frac{c^2 (3 b B+A c)}{x^4}+\frac{B c^3}{x^3}\right ) \, dx\\ &=-\frac{A b^3}{6 x^6}-\frac{b^2 (b B+3 A c)}{5 x^5}-\frac{3 b c (b B+A c)}{4 x^4}-\frac{c^2 (3 b B+A c)}{3 x^3}-\frac{B c^3}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0201825, size = 74, normalized size = 0.99 \[ -\frac{A \left (36 b^2 c x+10 b^3+45 b c^2 x^2+20 c^3 x^3\right )+3 B x \left (15 b^2 c x+4 b^3+20 b c^2 x^2+10 c^3 x^3\right )}{60 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 66, normalized size = 0.9 \begin{align*} -{\frac{A{b}^{3}}{6\,{x}^{6}}}-{\frac{{b}^{2} \left ( 3\,Ac+bB \right ) }{5\,{x}^{5}}}-{\frac{3\,bc \left ( Ac+bB \right ) }{4\,{x}^{4}}}-{\frac{{c}^{2} \left ( Ac+3\,bB \right ) }{3\,{x}^{3}}}-{\frac{B{c}^{3}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05769, size = 99, normalized size = 1.32 \begin{align*} -\frac{30 \, B c^{3} x^{4} + 10 \, A b^{3} + 20 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 45 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 12 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72531, size = 165, normalized size = 2.2 \begin{align*} -\frac{30 \, B c^{3} x^{4} + 10 \, A b^{3} + 20 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 45 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 12 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.55909, size = 78, normalized size = 1.04 \begin{align*} - \frac{10 A b^{3} + 30 B c^{3} x^{4} + x^{3} \left (20 A c^{3} + 60 B b c^{2}\right ) + x^{2} \left (45 A b c^{2} + 45 B b^{2} c\right ) + x \left (36 A b^{2} c + 12 B b^{3}\right )}{60 x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12239, size = 101, normalized size = 1.35 \begin{align*} -\frac{30 \, B c^{3} x^{4} + 60 \, B b c^{2} x^{3} + 20 \, A c^{3} x^{3} + 45 \, B b^{2} c x^{2} + 45 \, A b c^{2} x^{2} + 12 \, B b^{3} x + 36 \, A b^{2} c x + 10 \, A b^{3}}{60 \, x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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