Optimal. Leaf size=143 \[ -\frac {a^6 A}{10 x^{10}}-\frac {a^5 (a B+6 A b)}{9 x^9}-\frac {3 a^4 b (2 a B+5 A b)}{8 x^8}-\frac {5 a^3 b^2 (3 a B+4 A b)}{7 x^7}-\frac {5 a^2 b^3 (4 a B+3 A b)}{6 x^6}-\frac {b^5 (6 a B+A b)}{4 x^4}-\frac {3 a b^4 (5 a B+2 A b)}{5 x^5}-\frac {b^6 B}{3 x^3} \]
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Rubi [A] time = 0.08, antiderivative size = 143, 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 {5 a^3 b^2 (3 a B+4 A b)}{7 x^7}-\frac {5 a^2 b^3 (4 a B+3 A b)}{6 x^6}-\frac {a^5 (a B+6 A b)}{9 x^9}-\frac {3 a^4 b (2 a B+5 A b)}{8 x^8}-\frac {a^6 A}{10 x^{10}}-\frac {3 a b^4 (5 a B+2 A b)}{5 x^5}-\frac {b^5 (6 a B+A b)}{4 x^4}-\frac {b^6 B}{3 x^3} \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 )^3}{x^{11}} \, dx &=\int \frac {(a+b x)^6 (A+B x)}{x^{11}} \, dx\\ &=\int \left (\frac {a^6 A}{x^{11}}+\frac {a^5 (6 A b+a B)}{x^{10}}+\frac {3 a^4 b (5 A b+2 a B)}{x^9}+\frac {5 a^3 b^2 (4 A b+3 a B)}{x^8}+\frac {5 a^2 b^3 (3 A b+4 a B)}{x^7}+\frac {3 a b^4 (2 A b+5 a B)}{x^6}+\frac {b^5 (A b+6 a B)}{x^5}+\frac {b^6 B}{x^4}\right ) \, dx\\ &=-\frac {a^6 A}{10 x^{10}}-\frac {a^5 (6 A b+a B)}{9 x^9}-\frac {3 a^4 b (5 A b+2 a B)}{8 x^8}-\frac {5 a^3 b^2 (4 A b+3 a B)}{7 x^7}-\frac {5 a^2 b^3 (3 A b+4 a B)}{6 x^6}-\frac {3 a b^4 (2 A b+5 a B)}{5 x^5}-\frac {b^5 (A b+6 a B)}{4 x^4}-\frac {b^6 B}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 126, normalized size = 0.88 \begin {gather*} -\frac {28 a^6 (9 A+10 B x)+210 a^5 b x (8 A+9 B x)+675 a^4 b^2 x^2 (7 A+8 B x)+1200 a^3 b^3 x^3 (6 A+7 B x)+1260 a^2 b^4 x^4 (5 A+6 B x)+756 a b^5 x^5 (4 A+5 B x)+210 b^6 x^6 (3 A+4 B x)}{2520 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 )^3}{x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 147, normalized size = 1.03 \begin {gather*} -\frac {840 \, B b^{6} x^{7} + 252 \, A a^{6} + 630 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 1512 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 2100 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 1800 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 945 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 280 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x}{2520 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 147, normalized size = 1.03 \begin {gather*} -\frac {840 \, B b^{6} x^{7} + 3780 \, B a b^{5} x^{6} + 630 \, A b^{6} x^{6} + 7560 \, B a^{2} b^{4} x^{5} + 3024 \, A a b^{5} x^{5} + 8400 \, B a^{3} b^{3} x^{4} + 6300 \, A a^{2} b^{4} x^{4} + 5400 \, B a^{4} b^{2} x^{3} + 7200 \, A a^{3} b^{3} x^{3} + 1890 \, B a^{5} b x^{2} + 4725 \, A a^{4} b^{2} x^{2} + 280 \, B a^{6} x + 1680 \, A a^{5} b x + 252 \, A a^{6}}{2520 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 128, normalized size = 0.90 \begin {gather*} -\frac {B \,b^{6}}{3 x^{3}}-\frac {\left (A b +6 B a \right ) b^{5}}{4 x^{4}}-\frac {3 \left (2 A b +5 B a \right ) a \,b^{4}}{5 x^{5}}-\frac {5 \left (3 A b +4 B a \right ) a^{2} b^{3}}{6 x^{6}}-\frac {5 \left (4 A b +3 B a \right ) a^{3} b^{2}}{7 x^{7}}-\frac {A \,a^{6}}{10 x^{10}}-\frac {3 \left (5 A b +2 B a \right ) a^{4} b}{8 x^{8}}-\frac {\left (6 A b +B a \right ) a^{5}}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 147, normalized size = 1.03 \begin {gather*} -\frac {840 \, B b^{6} x^{7} + 252 \, A a^{6} + 630 \, {\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 1512 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 2100 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 1800 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 945 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 280 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} x}{2520 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 143, normalized size = 1.00 \begin {gather*} -\frac {x\,\left (\frac {B\,a^6}{9}+\frac {2\,A\,b\,a^5}{3}\right )+\frac {A\,a^6}{10}+x^5\,\left (3\,B\,a^2\,b^4+\frac {6\,A\,a\,b^5}{5}\right )+x^2\,\left (\frac {3\,B\,a^5\,b}{4}+\frac {15\,A\,a^4\,b^2}{8}\right )+x^6\,\left (\frac {A\,b^6}{4}+\frac {3\,B\,a\,b^5}{2}\right )+x^4\,\left (\frac {10\,B\,a^3\,b^3}{3}+\frac {5\,A\,a^2\,b^4}{2}\right )+x^3\,\left (\frac {15\,B\,a^4\,b^2}{7}+\frac {20\,A\,a^3\,b^3}{7}\right )+\frac {B\,b^6\,x^7}{3}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 9.00, size = 158, normalized size = 1.10 \begin {gather*} \frac {- 252 A a^{6} - 840 B b^{6} x^{7} + x^{6} \left (- 630 A b^{6} - 3780 B a b^{5}\right ) + x^{5} \left (- 3024 A a b^{5} - 7560 B a^{2} b^{4}\right ) + x^{4} \left (- 6300 A a^{2} b^{4} - 8400 B a^{3} b^{3}\right ) + x^{3} \left (- 7200 A a^{3} b^{3} - 5400 B a^{4} b^{2}\right ) + x^{2} \left (- 4725 A a^{4} b^{2} - 1890 B a^{5} b\right ) + x \left (- 1680 A a^{5} b - 280 B a^{6}\right )}{2520 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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