Optimal. Leaf size=75 \[ -\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3} \]
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Rubi [A] time = 0.0408125, 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} \[ -\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3} \]
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^{11}} \, dx &=\int \left (\frac{A b^3}{x^8}+\frac{b^2 (b B+3 A c)}{x^7}+\frac{3 b c (b B+A c)}{x^6}+\frac{c^2 (3 b B+A c)}{x^5}+\frac{B c^3}{x^4}\right ) \, dx\\ &=-\frac{A b^3}{7 x^7}-\frac{b^2 (b B+3 A c)}{6 x^6}-\frac{3 b c (b B+A c)}{5 x^5}-\frac{c^2 (3 b B+A c)}{4 x^4}-\frac{B c^3}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0199361, size = 75, normalized size = 1. \[ -\frac{3 A \left (70 b^2 c x+20 b^3+84 b c^2 x^2+35 c^3 x^3\right )+7 B x \left (36 b^2 c x+10 b^3+45 b c^2 x^2+20 c^3 x^3\right )}{420 x^7} \]
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}}{7\,{x}^{7}}}-{\frac{{b}^{2} \left ( 3\,Ac+bB \right ) }{6\,{x}^{6}}}-{\frac{3\,bc \left ( Ac+bB \right ) }{5\,{x}^{5}}}-{\frac{{c}^{2} \left ( Ac+3\,bB \right ) }{4\,{x}^{4}}}-{\frac{B{c}^{3}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08281, size = 99, normalized size = 1.32 \begin{align*} -\frac{140 \, B c^{3} x^{4} + 60 \, A b^{3} + 105 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 252 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 70 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72633, size = 170, normalized size = 2.27 \begin{align*} -\frac{140 \, B c^{3} x^{4} + 60 \, A b^{3} + 105 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 252 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 70 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.8193, size = 78, normalized size = 1.04 \begin{align*} - \frac{60 A b^{3} + 140 B c^{3} x^{4} + x^{3} \left (105 A c^{3} + 315 B b c^{2}\right ) + x^{2} \left (252 A b c^{2} + 252 B b^{2} c\right ) + x \left (210 A b^{2} c + 70 B b^{3}\right )}{420 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16938, size = 101, normalized size = 1.35 \begin{align*} -\frac{140 \, B c^{3} x^{4} + 315 \, B b c^{2} x^{3} + 105 \, A c^{3} x^{3} + 252 \, B b^{2} c x^{2} + 252 \, A b c^{2} x^{2} + 70 \, B b^{3} x + 210 \, A b^{2} c x + 60 \, A b^{3}}{420 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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