Optimal. Leaf size=47 \[ -\frac {a B+A b}{6 x^6}-\frac {a A}{7 x^7}-\frac {A c+b B}{5 x^5}-\frac {B c}{4 x^4} \]
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Rubi [A] time = 0.03, 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}{6 x^6}-\frac {a A}{7 x^7}-\frac {A c+b B}{5 x^5}-\frac {B c}{4 x^4} \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^8} \, dx &=\int \left (\frac {a A}{x^8}+\frac {A b+a B}{x^7}+\frac {b B+A c}{x^6}+\frac {B c}{x^5}\right ) \, dx\\ &=-\frac {a A}{7 x^7}-\frac {A b+a B}{6 x^6}-\frac {b B+A c}{5 x^5}-\frac {B c}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 0.98 \begin {gather*} -\frac {10 a (6 A+7 B x)+7 x (2 A (5 b+6 c x)+3 B x (4 b+5 c x))}{420 x^7} \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^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.38, size = 39, normalized size = 0.83 \begin {gather*} -\frac {105 \, B c x^{3} + 84 \, {\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \, {\left (B a + A b\right )} x}{420 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 41, normalized size = 0.87 \begin {gather*} -\frac {105 \, B c x^{3} + 84 \, B b x^{2} + 84 \, A c x^{2} + 70 \, B a x + 70 \, A b x + 60 \, A a}{420 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 40, normalized size = 0.85 \begin {gather*} -\frac {B c}{4 x^{4}}-\frac {A a}{7 x^{7}}-\frac {A c +b B}{5 x^{5}}-\frac {A b +B a}{6 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 39, normalized size = 0.83 \begin {gather*} -\frac {105 \, B c x^{3} + 84 \, {\left (B b + A c\right )} x^{2} + 60 \, A a + 70 \, {\left (B a + A b\right )} x}{420 \, x^{7}} \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}{4}+\left (\frac {A\,c}{5}+\frac {B\,b}{5}\right )\,x^2+\left (\frac {A\,b}{6}+\frac {B\,a}{6}\right )\,x+\frac {A\,a}{7}}{x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.87, size = 46, normalized size = 0.98 \begin {gather*} \frac {- 60 A a - 105 B c x^{3} + x^{2} \left (- 84 A c - 84 B b\right ) + x \left (- 70 A b - 70 B a\right )}{420 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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