Optimal. Leaf size=166 \[ -\frac {a^3 A}{9 x^9}-\frac {a^2 (a B+3 A b)}{8 x^8}-\frac {3 a \left (A \left (a c+b^2\right )+a b B\right )}{7 x^7}-\frac {3 c \left (a B c+A b c+b^2 B\right )}{4 x^4}-\frac {3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\frac {A \left (6 a b c+b^3\right )+3 a B \left (a c+b^2\right )}{6 x^6}-\frac {c^2 (A c+3 b B)}{3 x^3}-\frac {B c^3}{2 x^2} \]
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Rubi [A] time = 0.11, antiderivative size = 166, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\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} \end {gather*}
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*}
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Mathematica [A] time = 0.06, size = 175, normalized size = 1.05 \begin {gather*} -\frac {35 a^3 (8 A+9 B x)+45 a^2 x (3 A (7 b+8 c x)+4 B x (6 b+7 c 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 (10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right )+3 B x \left (4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right )\right )}{2520 x^9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(A+B x) \left (a+b x+c x^2\right )^3}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.41, size = 166, normalized size = 1.00 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 191, normalized size = 1.15 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 154, normalized size = 0.93 \begin {gather*} -\frac {B \,c^{3}}{2 x^{2}}-\frac {\left (A c +3 b B \right ) c^{2}}{3 x^{3}}-\frac {3 \left (A b c +a B c +b^{2} B \right ) c}{4 x^{4}}-\frac {A \,a^{3}}{9 x^{9}}-\frac {3 A a \,c^{2}+3 A \,b^{2} c +6 a b B c +b^{3} B}{5 x^{5}}-\frac {\left (3 A b +B a \right ) a^{2}}{8 x^{8}}-\frac {3 \left (A a c +A \,b^{2}+B a b \right ) a}{7 x^{7}}-\frac {6 A a b c +A \,b^{3}+3 B \,a^{2} c +3 B a \,b^{2}}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 166, normalized size = 1.00 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 167, normalized size = 1.01 \begin {gather*} -\frac {x^3\,\left (\frac {B\,c\,a^2}{2}+\frac {B\,a\,b^2}{2}+A\,c\,a\,b+\frac {A\,b^3}{6}\right )+x^4\,\left (\frac {B\,b^3}{5}+\frac {3\,A\,b^2\,c}{5}+\frac {6\,B\,a\,b\,c}{5}+\frac {3\,A\,a\,c^2}{5}\right )+x\,\left (\frac {B\,a^3}{8}+\frac {3\,A\,b\,a^2}{8}\right )+\frac {A\,a^3}{9}+x^6\,\left (\frac {A\,c^3}{3}+B\,b\,c^2\right )+x^2\,\left (\frac {3\,B\,a^2\,b}{7}+\frac {3\,A\,c\,a^2}{7}+\frac {3\,A\,a\,b^2}{7}\right )+x^5\,\left (\frac {3\,B\,b^2\,c}{4}+\frac {3\,A\,b\,c^2}{4}+\frac {3\,B\,a\,c^2}{4}\right )+\frac {B\,c^3\,x^7}{2}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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