Optimal. Leaf size=113 \[ -\frac {a^5 A}{19 x^{19}}-\frac {a^4 (a B+5 A b)}{16 x^{16}}-\frac {5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac {a^2 b^2 (a B+A b)}{x^{10}}-\frac {b^4 (5 a B+A b)}{4 x^4}-\frac {5 a b^3 (2 a B+A b)}{7 x^7}-\frac {b^5 B}{x} \]
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Rubi [A] time = 0.06, antiderivative size = 113, 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} \[ -\frac {a^2 b^2 (a B+A b)}{x^{10}}-\frac {a^4 (a B+5 A b)}{16 x^{16}}-\frac {5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac {a^5 A}{19 x^{19}}-\frac {5 a b^3 (2 a B+A b)}{7 x^7}-\frac {b^4 (5 a B+A b)}{4 x^4}-\frac {b^5 B}{x} \]
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^{20}} \, dx &=\int \left (\frac {a^5 A}{x^{20}}+\frac {a^4 (5 A b+a B)}{x^{17}}+\frac {5 a^3 b (2 A b+a B)}{x^{14}}+\frac {10 a^2 b^2 (A b+a B)}{x^{11}}+\frac {5 a b^3 (A b+2 a B)}{x^8}+\frac {b^4 (A b+5 a B)}{x^5}+\frac {b^5 B}{x^2}\right ) \, dx\\ &=-\frac {a^5 A}{19 x^{19}}-\frac {a^4 (5 A b+a B)}{16 x^{16}}-\frac {5 a^3 b (2 A b+a B)}{13 x^{13}}-\frac {a^2 b^2 (A b+a B)}{x^{10}}-\frac {5 a b^3 (A b+2 a B)}{7 x^7}-\frac {b^4 (A b+5 a B)}{4 x^4}-\frac {b^5 B}{x}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 119, normalized size = 1.05 \[ -\frac {91 a^5 \left (16 A+19 B x^3\right )+665 a^4 b x^3 \left (13 A+16 B x^3\right )+2128 a^3 b^2 x^6 \left (10 A+13 B x^3\right )+3952 a^2 b^3 x^9 \left (7 A+10 B x^3\right )+4940 a b^4 x^{12} \left (4 A+7 B x^3\right )+6916 b^5 x^{15} \left (A+4 B x^3\right )}{27664 x^{19}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.25, size = 121, normalized size = 1.07 \[ -\frac {27664 \, B b^{5} x^{18} + 6916 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 19760 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 27664 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 10640 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 1456 \, A a^{5} + 1729 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{27664 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 127, normalized size = 1.12 \[ -\frac {27664 \, B b^{5} x^{18} + 34580 \, B a b^{4} x^{15} + 6916 \, A b^{5} x^{15} + 39520 \, B a^{2} b^{3} x^{12} + 19760 \, A a b^{4} x^{12} + 27664 \, B a^{3} b^{2} x^{9} + 27664 \, A a^{2} b^{3} x^{9} + 10640 \, B a^{4} b x^{6} + 21280 \, A a^{3} b^{2} x^{6} + 1729 \, B a^{5} x^{3} + 8645 \, A a^{4} b x^{3} + 1456 \, A a^{5}}{27664 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 104, normalized size = 0.92 \[ -\frac {B \,b^{5}}{x}-\frac {\left (A b +5 B a \right ) b^{4}}{4 x^{4}}-\frac {5 \left (A b +2 B a \right ) a \,b^{3}}{7 x^{7}}-\frac {\left (A b +B a \right ) a^{2} b^{2}}{x^{10}}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{13 x^{13}}-\frac {\left (5 A b +B a \right ) a^{4}}{16 x^{16}}-\frac {A \,a^{5}}{19 x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 121, normalized size = 1.07 \[ -\frac {27664 \, B b^{5} x^{18} + 6916 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 19760 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 27664 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 10640 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 1456 \, A a^{5} + 1729 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{27664 \, x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.37, size = 119, normalized size = 1.05 \[ -\frac {\frac {A\,a^5}{19}+x^{12}\,\left (\frac {10\,B\,a^2\,b^3}{7}+\frac {5\,A\,a\,b^4}{7}\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{13}+\frac {10\,A\,a^3\,b^2}{13}\right )+x^3\,\left (\frac {B\,a^5}{16}+\frac {5\,A\,b\,a^4}{16}\right )+x^{15}\,\left (\frac {A\,b^5}{4}+\frac {5\,B\,a\,b^4}{4}\right )+x^9\,\left (B\,a^3\,b^2+A\,a^2\,b^3\right )+B\,b^5\,x^{18}}{x^{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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