Optimal. Leaf size=117 \[ \frac {1}{4} a^5 A x^4+\frac {1}{7} a^4 x^7 (a B+5 A b)+\frac {1}{2} a^3 b x^{10} (a B+2 A b)+\frac {10}{13} a^2 b^2 x^{13} (a B+A b)+\frac {1}{19} b^4 x^{19} (5 a B+A b)+\frac {5}{16} a b^3 x^{16} (2 a B+A b)+\frac {1}{22} b^5 B x^{22} \]
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Rubi [A] time = 0.07, antiderivative size = 117, 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}{13} a^2 b^2 x^{13} (a B+A b)+\frac {1}{2} a^3 b x^{10} (a B+2 A b)+\frac {1}{7} a^4 x^7 (a B+5 A b)+\frac {1}{4} a^5 A x^4+\frac {1}{19} b^4 x^{19} (5 a B+A b)+\frac {5}{16} a b^3 x^{16} (2 a B+A b)+\frac {1}{22} b^5 B x^{22} \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x^3 \left (a+b x^3\right )^5 \left (A+B x^3\right ) \, dx &=\int \left (a^5 A x^3+a^4 (5 A b+a B) x^6+5 a^3 b (2 A b+a B) x^9+10 a^2 b^2 (A b+a B) x^{12}+5 a b^3 (A b+2 a B) x^{15}+b^4 (A b+5 a B) x^{18}+b^5 B x^{21}\right ) \, dx\\ &=\frac {1}{4} a^5 A x^4+\frac {1}{7} a^4 (5 A b+a B) x^7+\frac {1}{2} a^3 b (2 A b+a B) x^{10}+\frac {10}{13} a^2 b^2 (A b+a B) x^{13}+\frac {5}{16} a b^3 (A b+2 a B) x^{16}+\frac {1}{19} b^4 (A b+5 a B) x^{19}+\frac {1}{22} b^5 B x^{22}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 117, normalized size = 1.00 \begin {gather*} \frac {1}{4} a^5 A x^4+\frac {1}{7} a^4 x^7 (a B+5 A b)+\frac {1}{2} a^3 b x^{10} (a B+2 A b)+\frac {10}{13} a^2 b^2 x^{13} (a B+A b)+\frac {1}{19} b^4 x^{19} (5 a B+A b)+\frac {5}{16} a b^3 x^{16} (2 a B+A b)+\frac {1}{22} b^5 B x^{22} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^3 \left (a+b x^3\right )^5 \left (A+B x^3\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.75, size = 124, normalized size = 1.06 \begin {gather*} \frac {1}{22} x^{22} b^{5} B + \frac {5}{19} x^{19} b^{4} a B + \frac {1}{19} x^{19} b^{5} A + \frac {5}{8} x^{16} b^{3} a^{2} B + \frac {5}{16} x^{16} b^{4} a A + \frac {10}{13} x^{13} b^{2} a^{3} B + \frac {10}{13} x^{13} b^{3} a^{2} A + \frac {1}{2} x^{10} b a^{4} B + x^{10} b^{2} a^{3} A + \frac {1}{7} x^{7} a^{5} B + \frac {5}{7} x^{7} b a^{4} A + \frac {1}{4} x^{4} a^{5} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 124, normalized size = 1.06 \begin {gather*} \frac {1}{22} \, B b^{5} x^{22} + \frac {5}{19} \, B a b^{4} x^{19} + \frac {1}{19} \, A b^{5} x^{19} + \frac {5}{8} \, B a^{2} b^{3} x^{16} + \frac {5}{16} \, A a b^{4} x^{16} + \frac {10}{13} \, B a^{3} b^{2} x^{13} + \frac {10}{13} \, A a^{2} b^{3} x^{13} + \frac {1}{2} \, B a^{4} b x^{10} + A a^{3} b^{2} x^{10} + \frac {1}{7} \, B a^{5} x^{7} + \frac {5}{7} \, A a^{4} b x^{7} + \frac {1}{4} \, A a^{5} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 124, normalized size = 1.06 \begin {gather*} \frac {B \,b^{5} x^{22}}{22}+\frac {\left (b^{5} A +5 a \,b^{4} B \right ) x^{19}}{19}+\frac {\left (5 a \,b^{4} A +10 a^{2} b^{3} B \right ) x^{16}}{16}+\frac {\left (10 a^{2} b^{3} A +10 a^{3} b^{2} B \right ) x^{13}}{13}+\frac {A \,a^{5} x^{4}}{4}+\frac {\left (10 a^{3} b^{2} A +5 a^{4} b B \right ) x^{10}}{10}+\frac {\left (5 a^{4} b A +a^{5} B \right ) x^{7}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 119, normalized size = 1.02 \begin {gather*} \frac {1}{22} \, B b^{5} x^{22} + \frac {1}{19} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{19} + \frac {5}{16} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{16} + \frac {10}{13} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{13} + \frac {1}{2} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{10} + \frac {1}{4} \, A a^{5} x^{4} + \frac {1}{7} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 107, normalized size = 0.91 \begin {gather*} x^7\,\left (\frac {B\,a^5}{7}+\frac {5\,A\,b\,a^4}{7}\right )+x^{19}\,\left (\frac {A\,b^5}{19}+\frac {5\,B\,a\,b^4}{19}\right )+\frac {A\,a^5\,x^4}{4}+\frac {B\,b^5\,x^{22}}{22}+\frac {10\,a^2\,b^2\,x^{13}\,\left (A\,b+B\,a\right )}{13}+\frac {a^3\,b\,x^{10}\,\left (2\,A\,b+B\,a\right )}{2}+\frac {5\,a\,b^3\,x^{16}\,\left (A\,b+2\,B\,a\right )}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 133, normalized size = 1.14 \begin {gather*} \frac {A a^{5} x^{4}}{4} + \frac {B b^{5} x^{22}}{22} + x^{19} \left (\frac {A b^{5}}{19} + \frac {5 B a b^{4}}{19}\right ) + x^{16} \left (\frac {5 A a b^{4}}{16} + \frac {5 B a^{2} b^{3}}{8}\right ) + x^{13} \left (\frac {10 A a^{2} b^{3}}{13} + \frac {10 B a^{3} b^{2}}{13}\right ) + x^{10} \left (A a^{3} b^{2} + \frac {B a^{4} b}{2}\right ) + x^{7} \left (\frac {5 A a^{4} b}{7} + \frac {B a^{5}}{7}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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