Optimal. Leaf size=99 \[ -\frac {a^4 A}{10 x^{10}}-\frac {a^3 (a B+4 A b)}{9 x^9}-\frac {a^2 b (2 a B+3 A b)}{4 x^8}-\frac {b^3 (4 a B+A b)}{6 x^6}-\frac {2 a b^2 (3 a B+2 A b)}{7 x^7}-\frac {b^4 B}{5 x^5} \]
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Rubi [A] time = 0.05, antiderivative size = 99, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {27, 76} \begin {gather*} -\frac {a^3 (a B+4 A b)}{9 x^9}-\frac {a^2 b (2 a B+3 A b)}{4 x^8}-\frac {a^4 A}{10 x^{10}}-\frac {2 a b^2 (3 a B+2 A b)}{7 x^7}-\frac {b^3 (4 a B+A b)}{6 x^6}-\frac {b^4 B}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 76
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^2}{x^{11}} \, dx &=\int \frac {(a+b x)^4 (A+B x)}{x^{11}} \, dx\\ &=\int \left (\frac {a^4 A}{x^{11}}+\frac {a^3 (4 A b+a B)}{x^{10}}+\frac {2 a^2 b (3 A b+2 a B)}{x^9}+\frac {2 a b^2 (2 A b+3 a B)}{x^8}+\frac {b^3 (A b+4 a B)}{x^7}+\frac {b^4 B}{x^6}\right ) \, dx\\ &=-\frac {a^4 A}{10 x^{10}}-\frac {a^3 (4 A b+a B)}{9 x^9}-\frac {a^2 b (3 A b+2 a B)}{4 x^8}-\frac {2 a b^2 (2 A b+3 a B)}{7 x^7}-\frac {b^3 (A b+4 a B)}{6 x^6}-\frac {b^4 B}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 88, normalized size = 0.89 \begin {gather*} -\frac {14 a^4 (9 A+10 B x)+70 a^3 b x (8 A+9 B x)+135 a^2 b^2 x^2 (7 A+8 B x)+120 a b^3 x^3 (6 A+7 B x)+42 b^4 x^4 (5 A+6 B x)}{1260 x^{10}} \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^2+2 a b x+b^2 x^2\right )^2}{x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 99, normalized size = 1.00 \begin {gather*} -\frac {252 \, B b^{4} x^{5} + 126 \, A a^{4} + 210 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 360 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 315 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 140 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 99, normalized size = 1.00 \begin {gather*} -\frac {252 \, B b^{4} x^{5} + 840 \, B a b^{3} x^{4} + 210 \, A b^{4} x^{4} + 1080 \, B a^{2} b^{2} x^{3} + 720 \, A a b^{3} x^{3} + 630 \, B a^{3} b x^{2} + 945 \, A a^{2} b^{2} x^{2} + 140 \, B a^{4} x + 560 \, A a^{3} b x + 126 \, A a^{4}}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 88, normalized size = 0.89 \begin {gather*} -\frac {B \,b^{4}}{5 x^{5}}-\frac {\left (A b +4 B a \right ) b^{3}}{6 x^{6}}-\frac {2 \left (2 A b +3 B a \right ) a \,b^{2}}{7 x^{7}}-\frac {A \,a^{4}}{10 x^{10}}-\frac {\left (3 A b +2 B a \right ) a^{2} b}{4 x^{8}}-\frac {\left (4 A b +B a \right ) a^{3}}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 99, normalized size = 1.00 \begin {gather*} -\frac {252 \, B b^{4} x^{5} + 126 \, A a^{4} + 210 \, {\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 360 \, {\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} + 315 \, {\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 140 \, {\left (B a^{4} + 4 \, A a^{3} b\right )} x}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 97, normalized size = 0.98 \begin {gather*} -\frac {x\,\left (\frac {B\,a^4}{9}+\frac {4\,A\,b\,a^3}{9}\right )+\frac {A\,a^4}{10}+x^2\,\left (\frac {B\,a^3\,b}{2}+\frac {3\,A\,a^2\,b^2}{4}\right )+x^3\,\left (\frac {6\,B\,a^2\,b^2}{7}+\frac {4\,A\,a\,b^3}{7}\right )+x^4\,\left (\frac {A\,b^4}{6}+\frac {2\,B\,a\,b^3}{3}\right )+\frac {B\,b^4\,x^5}{5}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.45, size = 107, normalized size = 1.08 \begin {gather*} \frac {- 126 A a^{4} - 252 B b^{4} x^{5} + x^{4} \left (- 210 A b^{4} - 840 B a b^{3}\right ) + x^{3} \left (- 720 A a b^{3} - 1080 B a^{2} b^{2}\right ) + x^{2} \left (- 945 A a^{2} b^{2} - 630 B a^{3} b\right ) + x \left (- 560 A a^{3} b - 140 B a^{4}\right )}{1260 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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