Optimal. Leaf size=47 \[ -\frac {a B+A b}{4 x^4}-\frac {a A}{5 x^5}-\frac {A c+b B}{3 x^3}-\frac {B c}{2 x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {765} \begin {gather*} -\frac {a B+A b}{4 x^4}-\frac {a A}{5 x^5}-\frac {A c+b B}{3 x^3}-\frac {B c}{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 )}{x^6} \, dx &=\int \left (\frac {a A}{x^6}+\frac {A b+a B}{x^5}+\frac {b B+A c}{x^4}+\frac {B c}{x^3}\right ) \, dx\\ &=-\frac {a A}{5 x^5}-\frac {A b+a B}{4 x^4}-\frac {b B+A c}{3 x^3}-\frac {B c}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 44, normalized size = 0.94 \begin {gather*} -\frac {3 a (4 A+5 B x)+5 x \left (3 A b+4 A c x+4 b B x+6 B c x^2\right )}{60 x^5} \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 )}{x^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 39, normalized size = 0.83 \begin {gather*} -\frac {30 \, B c x^{3} + 20 \, {\left (B b + A c\right )} x^{2} + 12 \, A a + 15 \, {\left (B a + A b\right )} x}{60 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 41, normalized size = 0.87 \begin {gather*} -\frac {30 \, B c x^{3} + 20 \, B b x^{2} + 20 \, A c x^{2} + 15 \, B a x + 15 \, A b x + 12 \, A a}{60 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 40, normalized size = 0.85 \begin {gather*} -\frac {B c}{2 x^{2}}-\frac {A a}{5 x^{5}}-\frac {A c +b B}{3 x^{3}}-\frac {A b +B a}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 39, normalized size = 0.83 \begin {gather*} -\frac {30 \, B c x^{3} + 20 \, {\left (B b + A c\right )} x^{2} + 12 \, A a + 15 \, {\left (B a + A b\right )} x}{60 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 41, normalized size = 0.87 \begin {gather*} -\frac {\frac {B\,c\,x^3}{2}+\left (\frac {A\,c}{3}+\frac {B\,b}{3}\right )\,x^2+\left (\frac {A\,b}{4}+\frac {B\,a}{4}\right )\,x+\frac {A\,a}{5}}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.70, size = 46, normalized size = 0.98 \begin {gather*} \frac {- 12 A a - 30 B c x^{3} + x^{2} \left (- 20 A c - 20 B b\right ) + x \left (- 15 A b - 15 B a\right )}{60 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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