Optimal. Leaf size=75 \[ -\frac {A b^3}{6 x^6}-\frac {b^2 (3 A c+b B)}{5 x^5}-\frac {c^2 (A c+3 b B)}{3 x^3}-\frac {3 b c (A c+b B)}{4 x^4}-\frac {B c^3}{2 x^2} \]
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Rubi [A] time = 0.04, antiderivative size = 75, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.02, size = 74, normalized size = 0.99 \[ -\frac {A \left (10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right )+3 B x \left (4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right )}{60 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 73, normalized size = 0.97 \[ -\frac {30 \, B c^{3} x^{4} + 10 \, A b^{3} + 20 \, {\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 45 \, {\left (B b^{2} c + A b c^{2}\right )} x^{2} + 12 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 75, normalized size = 1.00 \[ -\frac {30 \, B c^{3} x^{4} + 60 \, B b c^{2} x^{3} + 20 \, A c^{3} x^{3} + 45 \, B b^{2} c x^{2} + 45 \, A b c^{2} x^{2} + 12 \, B b^{3} x + 36 \, A b^{2} c x + 10 \, A b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 66, normalized size = 0.88 \[ -\frac {B \,c^{3}}{2 x^{2}}-\frac {\left (A c +3 b B \right ) c^{2}}{3 x^{3}}-\frac {A \,b^{3}}{6 x^{6}}-\frac {3 \left (A c +b B \right ) b c}{4 x^{4}}-\frac {\left (3 A c +b B \right ) b^{2}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 73, normalized size = 0.97 \[ -\frac {30 \, B c^{3} x^{4} + 10 \, A b^{3} + 20 \, {\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 45 \, {\left (B b^{2} c + A b c^{2}\right )} x^{2} + 12 \, {\left (B b^{3} + 3 \, A b^{2} c\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 73, normalized size = 0.97 \[ -\frac {x^2\,\left (\frac {3\,B\,b^2\,c}{4}+\frac {3\,A\,b\,c^2}{4}\right )+x\,\left (\frac {B\,b^3}{5}+\frac {3\,A\,c\,b^2}{5}\right )+\frac {A\,b^3}{6}+x^3\,\left (\frac {A\,c^3}{3}+B\,b\,c^2\right )+\frac {B\,c^3\,x^4}{2}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.63, size = 82, normalized size = 1.09 \[ \frac {- 10 A b^{3} - 30 B c^{3} x^{4} + x^{3} \left (- 20 A c^{3} - 60 B b c^{2}\right ) + x^{2} \left (- 45 A b c^{2} - 45 B b^{2} c\right ) + x \left (- 36 A b^{2} c - 12 B b^{3}\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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