Optimal. Leaf size=75 \[ -\frac {a^3 A}{8 x^8}-\frac {a^2 (a B+3 A b)}{7 x^7}-\frac {b^2 (3 a B+A b)}{5 x^5}-\frac {a b (a B+A b)}{2 x^6}-\frac {b^3 B}{4 x^4} \]
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Rubi [A] time = 0.03, antiderivative size = 75, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {76} \begin {gather*} -\frac {a^2 (a B+3 A b)}{7 x^7}-\frac {a^3 A}{8 x^8}-\frac {b^2 (3 a B+A b)}{5 x^5}-\frac {a b (a B+A b)}{2 x^6}-\frac {b^3 B}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin {align*} \int \frac {(a+b x)^3 (A+B x)}{x^9} \, dx &=\int \left (\frac {a^3 A}{x^9}+\frac {a^2 (3 A b+a B)}{x^8}+\frac {3 a b (A b+a B)}{x^7}+\frac {b^2 (A b+3 a B)}{x^6}+\frac {b^3 B}{x^5}\right ) \, dx\\ &=-\frac {a^3 A}{8 x^8}-\frac {a^2 (3 A b+a B)}{7 x^7}-\frac {a b (A b+a B)}{2 x^6}-\frac {b^2 (A b+3 a B)}{5 x^5}-\frac {b^3 B}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 69, normalized size = 0.92 \begin {gather*} -\frac {5 a^3 (7 A+8 B x)+20 a^2 b x (6 A+7 B x)+28 a b^2 x^2 (5 A+6 B x)+14 b^3 x^3 (4 A+5 B x)}{280 x^8} \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)^3 (A+B x)}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.23, size = 73, normalized size = 0.97 \begin {gather*} -\frac {70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 75, normalized size = 1.00 \begin {gather*} -\frac {70 \, B b^{3} x^{4} + 168 \, B a b^{2} x^{3} + 56 \, A b^{3} x^{3} + 140 \, B a^{2} b x^{2} + 140 \, A a b^{2} x^{2} + 40 \, B a^{3} x + 120 \, A a^{2} b x + 35 \, A a^{3}}{280 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 66, normalized size = 0.88 \begin {gather*} -\frac {B \,b^{3}}{4 x^{4}}-\frac {\left (A b +3 B a \right ) b^{2}}{5 x^{5}}-\frac {A \,a^{3}}{8 x^{8}}-\frac {\left (A b +B a \right ) a b}{2 x^{6}}-\frac {\left (3 A b +B a \right ) a^{2}}{7 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 73, normalized size = 0.97 \begin {gather*} -\frac {70 \, B b^{3} x^{4} + 35 \, A a^{3} + 56 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 140 \, {\left (B a^{2} b + A a b^{2}\right )} x^{2} + 40 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x}{280 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 74, normalized size = 0.99 \begin {gather*} -\frac {x^2\,\left (\frac {B\,a^2\,b}{2}+\frac {A\,a\,b^2}{2}\right )+x\,\left (\frac {B\,a^3}{7}+\frac {3\,A\,b\,a^2}{7}\right )+\frac {A\,a^3}{8}+x^3\,\left (\frac {A\,b^3}{5}+\frac {3\,B\,a\,b^2}{5}\right )+\frac {B\,b^3\,x^4}{4}}{x^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.76, size = 82, normalized size = 1.09 \begin {gather*} \frac {- 35 A a^{3} - 70 B b^{3} x^{4} + x^{3} \left (- 56 A b^{3} - 168 B a b^{2}\right ) + x^{2} \left (- 140 A a b^{2} - 140 B a^{2} b\right ) + x \left (- 120 A a^{2} b - 40 B a^{3}\right )}{280 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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