Optimal. Leaf size=31 \[ -\frac {A c+b B}{2 x^2}-\frac {A b}{3 x^3}-\frac {B c}{x} \]
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Rubi [A] time = 0.02, antiderivative size = 31, 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}{2 x^2}-\frac {A b}{3 x^3}-\frac {B c}{x} \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^5} \, dx &=\int \left (\frac {A b}{x^4}+\frac {b B+A c}{x^3}+\frac {B c}{x^2}\right ) \, dx\\ &=-\frac {A b}{3 x^3}-\frac {b B+A c}{2 x^2}-\frac {B c}{x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.90 \begin {gather*} -\frac {A (2 b+3 c x)+3 B x (b+2 c x)}{6 x^3} \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^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 27, normalized size = 0.87 \begin {gather*} -\frac {6 \, B c x^{2} + 2 \, A b + 3 \, {\left (B b + A c\right )} x}{6 \, x^{3}} \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 = 0.87 \begin {gather*} -\frac {6 \, B c x^{2} + 3 \, B b x + 3 \, A c x + 2 \, A b}{6 \, x^{3}} \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 = 0.90 \begin {gather*} -\frac {B c}{x}-\frac {A b}{3 x^{3}}-\frac {A c +b B}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 27, normalized size = 0.87 \begin {gather*} -\frac {6 \, B c x^{2} + 2 \, A b + 3 \, {\left (B b + A c\right )} x}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 27, normalized size = 0.87 \begin {gather*} -\frac {B\,c\,x^2+\left (\frac {A\,c}{2}+\frac {B\,b}{2}\right )\,x+\frac {A\,b}{3}}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 31, normalized size = 1.00 \begin {gather*} \frac {- 2 A b - 6 B c x^{2} + x \left (- 3 A c - 3 B b\right )}{6 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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