Optimal. Leaf size=33 \[ -\frac {A c+b B}{4 x^4}-\frac {A b}{5 x^5}-\frac {B c}{3 x^3} \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {765} \begin {gather*} -\frac {A c+b B}{4 x^4}-\frac {A b}{5 x^5}-\frac {B c}{3 x^3} \end {gather*}
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 )}{x^7} \, dx &=\int \left (\frac {A b}{x^6}+\frac {b B+A c}{x^5}+\frac {B c}{x^4}\right ) \, dx\\ &=-\frac {A b}{5 x^5}-\frac {b B+A c}{4 x^4}-\frac {B c}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 0.94 \begin {gather*} -\frac {3 A (4 b+5 c x)+5 B x (3 b+4 c x)}{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 (b x+c x^2\right )}{x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 27, normalized size = 0.82 \begin {gather*} -\frac {20 \, B c x^{2} + 12 \, A b + 15 \, {\left (B b + A c\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 = 27, normalized size = 0.82 \begin {gather*} -\frac {20 \, B c x^{2} + 15 \, B b x + 15 \, A c x + 12 \, A b}{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 = 28, normalized size = 0.85 \begin {gather*} -\frac {B c}{3 x^{3}}-\frac {A b}{5 x^{5}}-\frac {A c +b B}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.91, size = 27, normalized size = 0.82 \begin {gather*} -\frac {20 \, B c x^{2} + 12 \, A b + 15 \, {\left (B b + A c\right )} x}{60 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \begin {gather*} -\frac {\frac {B\,c\,x^2}{3}+\left (\frac {A\,c}{4}+\frac {B\,b}{4}\right )\,x+\frac {A\,b}{5}}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 31, normalized size = 0.94 \begin {gather*} \frac {- 12 A b - 20 B c x^{2} + x \left (- 15 A c - 15 B b\right )}{60 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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