Optimal. Leaf size=115 \[ -\frac {a^5 A}{10 x^{10}}-\frac {a^4 (a B+5 A b)}{7 x^7}-\frac {5 a^3 b (a B+2 A b)}{4 x^4}-\frac {10 a^2 b^2 (a B+A b)}{x}+\frac {1}{5} b^4 x^5 (5 a B+A b)+\frac {5}{2} a b^3 x^2 (2 a B+A b)+\frac {1}{8} b^5 B x^8 \]
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Rubi [A] time = 0.06, antiderivative size = 115, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \begin {gather*} -\frac {10 a^2 b^2 (a B+A b)}{x}-\frac {5 a^3 b (a B+2 A b)}{4 x^4}-\frac {a^4 (a B+5 A b)}{7 x^7}-\frac {a^5 A}{10 x^{10}}+\frac {1}{5} b^4 x^5 (5 a B+A b)+\frac {5}{2} a b^3 x^2 (2 a B+A b)+\frac {1}{8} b^5 B x^8 \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{11}} \, dx &=\int \left (\frac {a^5 A}{x^{11}}+\frac {a^4 (5 A b+a B)}{x^8}+\frac {5 a^3 b (2 A b+a B)}{x^5}+\frac {10 a^2 b^2 (A b+a B)}{x^2}+5 a b^3 (A b+2 a B) x+b^4 (A b+5 a B) x^4+b^5 B x^7\right ) \, dx\\ &=-\frac {a^5 A}{10 x^{10}}-\frac {a^4 (5 A b+a B)}{7 x^7}-\frac {5 a^3 b (2 A b+a B)}{4 x^4}-\frac {10 a^2 b^2 (A b+a B)}{x}+\frac {5}{2} a b^3 (A b+2 a B) x^2+\frac {1}{5} b^4 (A b+5 a B) x^5+\frac {1}{8} b^5 B x^8\\ \end {align*}
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Mathematica [A] time = 0.02, size = 118, normalized size = 1.03 \begin {gather*} \frac {-4 a^5 \left (7 A+10 B x^3\right )-50 a^4 b x^3 \left (4 A+7 B x^3\right )-700 a^3 b^2 x^6 \left (A+4 B x^3\right )+1400 a^2 b^3 x^9 \left (B x^3-2 A\right )+140 a b^4 x^{12} \left (5 A+2 B x^3\right )+7 b^5 x^{15} \left (8 A+5 B x^3\right )}{280 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 {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.05, size = 121, normalized size = 1.05 \begin {gather*} \frac {35 \, B b^{5} x^{18} + 56 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 700 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 2800 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 350 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 28 \, A a^{5} - 40 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{280 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 127, normalized size = 1.10 \begin {gather*} \frac {1}{8} \, B b^{5} x^{8} + B a b^{4} x^{5} + \frac {1}{5} \, A b^{5} x^{5} + 5 \, B a^{2} b^{3} x^{2} + \frac {5}{2} \, A a b^{4} x^{2} - \frac {1400 \, B a^{3} b^{2} x^{9} + 1400 \, A a^{2} b^{3} x^{9} + 175 \, B a^{4} b x^{6} + 350 \, A a^{3} b^{2} x^{6} + 20 \, B a^{5} x^{3} + 100 \, A a^{4} b x^{3} + 14 \, A a^{5}}{140 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 111, normalized size = 0.97 \begin {gather*} \frac {B \,b^{5} x^{8}}{8}+\frac {A \,b^{5} x^{5}}{5}+B a \,b^{4} x^{5}+\frac {5 A a \,b^{4} x^{2}}{2}+5 B \,a^{2} b^{3} x^{2}-\frac {10 \left (A b +B a \right ) a^{2} b^{2}}{x}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{4 x^{4}}-\frac {\left (5 A b +B a \right ) a^{4}}{7 x^{7}}-\frac {A \,a^{5}}{10 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 122, normalized size = 1.06 \begin {gather*} \frac {1}{8} \, B b^{5} x^{8} + \frac {1}{5} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + \frac {5}{2} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{2} - \frac {1400 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 175 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 14 \, A a^{5} + 20 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{140 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.36, size = 118, normalized size = 1.03 \begin {gather*} x^5\,\left (\frac {A\,b^5}{5}+B\,a\,b^4\right )-\frac {\frac {A\,a^5}{10}+x^6\,\left (\frac {5\,B\,a^4\,b}{4}+\frac {5\,A\,a^3\,b^2}{2}\right )+x^3\,\left (\frac {B\,a^5}{7}+\frac {5\,A\,b\,a^4}{7}\right )+x^9\,\left (10\,B\,a^3\,b^2+10\,A\,a^2\,b^3\right )}{x^{10}}+\frac {B\,b^5\,x^8}{8}+\frac {5\,a\,b^3\,x^2\,\left (A\,b+2\,B\,a\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.93, size = 131, normalized size = 1.14 \begin {gather*} \frac {B b^{5} x^{8}}{8} + x^{5} \left (\frac {A b^{5}}{5} + B a b^{4}\right ) + x^{2} \left (\frac {5 A a b^{4}}{2} + 5 B a^{2} b^{3}\right ) + \frac {- 14 A a^{5} + x^{9} \left (- 1400 A a^{2} b^{3} - 1400 B a^{3} b^{2}\right ) + x^{6} \left (- 350 A a^{3} b^{2} - 175 B a^{4} b\right ) + x^{3} \left (- 100 A a^{4} b - 20 B a^{5}\right )}{140 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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