Optimal. Leaf size=166 \[ -\frac{a^2 (a B+3 A b)}{8 x^8}-\frac{a^3 A}{9 x^9}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\frac{3 a \left (A \left (a c+b^2\right )+a b B\right )}{7 x^7}-\frac{3 c \left (a B c+A b c+b^2 B\right )}{4 x^4}-\frac{A \left (6 a b c+b^3\right )+3 a B \left (a c+b^2\right )}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{B c^3}{2 x^2} \]
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Rubi [A] time = 0.105163, antiderivative size = 166, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {765} \[ -\frac{a^2 (a B+3 A b)}{8 x^8}-\frac{a^3 A}{9 x^9}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\frac{3 a \left (A \left (a c+b^2\right )+a b B\right )}{7 x^7}-\frac{3 c \left (a B c+A b c+b^2 B\right )}{4 x^4}-\frac{A \left (6 a b c+b^3\right )+3 a B \left (a c+b^2\right )}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{B c^3}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (a+b x+c x^2\right )^3}{x^{10}} \, dx &=\int \left (\frac{a^3 A}{x^{10}}+\frac{a^2 (3 A b+a B)}{x^9}+\frac{3 a \left (a b B+A \left (b^2+a c\right )\right )}{x^8}+\frac{3 a B \left (b^2+a c\right )+A \left (b^3+6 a b c\right )}{x^7}+\frac{b^3 B+3 A b^2 c+6 a b B c+3 a A c^2}{x^6}+\frac{3 c \left (b^2 B+A b c+a B c\right )}{x^5}+\frac{c^2 (3 b B+A c)}{x^4}+\frac{B c^3}{x^3}\right ) \, dx\\ &=-\frac{a^3 A}{9 x^9}-\frac{a^2 (3 A b+a B)}{8 x^8}-\frac{3 a \left (a b B+A \left (b^2+a c\right )\right )}{7 x^7}-\frac{3 a B \left (b^2+a c\right )+A \left (b^3+6 a b c\right )}{6 x^6}-\frac{b^3 B+3 A b^2 c+6 a b B c+3 a A c^2}{5 x^5}-\frac{3 c \left (b^2 B+A b c+a B c\right )}{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 = 0.0614397, size = 175, normalized size = 1.05 \[ -\frac{45 a^2 x (3 A (7 b+8 c x)+4 B x (6 b+7 c x))+35 a^3 (8 A+9 B x)+18 a x^2 \left (4 A \left (15 b^2+35 b c x+21 c^2 x^2\right )+7 B x \left (10 b^2+24 b c x+15 c^2 x^2\right )\right )+42 x^3 \left (A \left (36 b^2 c x+10 b^3+45 b c^2 x^2+20 c^3 x^3\right )+3 B x \left (15 b^2 c x+4 b^3+20 b c^2 x^2+10 c^3 x^3\right )\right )}{2520 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 154, normalized size = 0.9 \begin{align*} -{\frac{A{a}^{3}}{9\,{x}^{9}}}-{\frac{{c}^{2} \left ( Ac+3\,bB \right ) }{3\,{x}^{3}}}-{\frac{B{c}^{3}}{2\,{x}^{2}}}-{\frac{{a}^{2} \left ( 3\,Ab+aB \right ) }{8\,{x}^{8}}}-{\frac{3\,a \left ( aAc+A{b}^{2}+abB \right ) }{7\,{x}^{7}}}-{\frac{3\,aA{c}^{2}+3\,A{b}^{2}c+6\,abBc+{b}^{3}B}{5\,{x}^{5}}}-{\frac{3\,c \left ( Abc+aBc+{b}^{2}B \right ) }{4\,{x}^{4}}}-{\frac{6\,Aabc+A{b}^{3}+3\,B{a}^{2}c+3\,Ba{b}^{2}}{6\,{x}^{6}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06706, size = 224, normalized size = 1.35 \begin{align*} -\frac{1260 \, B c^{3} x^{7} + 840 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + 1890 \,{\left (B b^{2} c +{\left (B a + A b\right )} c^{2}\right )} x^{5} + 504 \,{\left (B b^{3} + 3 \, A a c^{2} + 3 \,{\left (2 \, B a b + A b^{2}\right )} c\right )} x^{4} + 280 \, A a^{3} + 420 \,{\left (3 \, B a b^{2} + A b^{3} + 3 \,{\left (B a^{2} + 2 \, A a b\right )} c\right )} x^{3} + 1080 \,{\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} x^{2} + 315 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{2520 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49143, size = 389, normalized size = 2.34 \begin{align*} -\frac{1260 \, B c^{3} x^{7} + 840 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{6} + 1890 \,{\left (B b^{2} c +{\left (B a + A b\right )} c^{2}\right )} x^{5} + 504 \,{\left (B b^{3} + 3 \, A a c^{2} + 3 \,{\left (2 \, B a b + A b^{2}\right )} c\right )} x^{4} + 280 \, A a^{3} + 420 \,{\left (3 \, B a b^{2} + A b^{3} + 3 \,{\left (B a^{2} + 2 \, A a b\right )} c\right )} x^{3} + 1080 \,{\left (B a^{2} b + A a b^{2} + A a^{2} c\right )} x^{2} + 315 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{2520 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25134, size = 258, normalized size = 1.55 \begin{align*} -\frac{1260 \, B c^{3} x^{7} + 2520 \, B b c^{2} x^{6} + 840 \, A c^{3} x^{6} + 1890 \, B b^{2} c x^{5} + 1890 \, B a c^{2} x^{5} + 1890 \, A b c^{2} x^{5} + 504 \, B b^{3} x^{4} + 3024 \, B a b c x^{4} + 1512 \, A b^{2} c x^{4} + 1512 \, A a c^{2} x^{4} + 1260 \, B a b^{2} x^{3} + 420 \, A b^{3} x^{3} + 1260 \, B a^{2} c x^{3} + 2520 \, A a b c x^{3} + 1080 \, B a^{2} b x^{2} + 1080 \, A a b^{2} x^{2} + 1080 \, A a^{2} c x^{2} + 315 \, B a^{3} x + 945 \, A a^{2} b x + 280 \, A a^{3}}{2520 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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