Optimal. Leaf size=117 \[ \frac {1}{2} a^5 A x^2+\frac {1}{5} a^4 x^5 (a B+5 A b)+\frac {5}{8} a^3 b x^8 (a B+2 A b)+\frac {10}{11} a^2 b^2 x^{11} (a B+A b)+\frac {1}{17} b^4 x^{17} (5 a B+A b)+\frac {5}{14} a b^3 x^{14} (2 a B+A b)+\frac {1}{20} b^5 B x^{20} \]
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Rubi [A] time = 0.06, antiderivative size = 117, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {448} \begin {gather*} \frac {10}{11} a^2 b^2 x^{11} (a B+A b)+\frac {5}{8} a^3 b x^8 (a B+2 A b)+\frac {1}{5} a^4 x^5 (a B+5 A b)+\frac {1}{2} a^5 A x^2+\frac {1}{17} b^4 x^{17} (5 a B+A b)+\frac {5}{14} a b^3 x^{14} (2 a B+A b)+\frac {1}{20} b^5 B x^{20} \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x \left (a+b x^3\right )^5 \left (A+B x^3\right ) \, dx &=\int \left (a^5 A x+a^4 (5 A b+a B) x^4+5 a^3 b (2 A b+a B) x^7+10 a^2 b^2 (A b+a B) x^{10}+5 a b^3 (A b+2 a B) x^{13}+b^4 (A b+5 a B) x^{16}+b^5 B x^{19}\right ) \, dx\\ &=\frac {1}{2} a^5 A x^2+\frac {1}{5} a^4 (5 A b+a B) x^5+\frac {5}{8} a^3 b (2 A b+a B) x^8+\frac {10}{11} a^2 b^2 (A b+a B) x^{11}+\frac {5}{14} a b^3 (A b+2 a B) x^{14}+\frac {1}{17} b^4 (A b+5 a B) x^{17}+\frac {1}{20} b^5 B x^{20}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 117, normalized size = 1.00 \begin {gather*} \frac {1}{2} a^5 A x^2+\frac {1}{5} a^4 x^5 (a B+5 A b)+\frac {5}{8} a^3 b x^8 (a B+2 A b)+\frac {10}{11} a^2 b^2 x^{11} (a B+A b)+\frac {1}{17} b^4 x^{17} (5 a B+A b)+\frac {5}{14} a b^3 x^{14} (2 a B+A b)+\frac {1}{20} b^5 B x^{20} \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 \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 = 0.70, size = 124, normalized size = 1.06 \begin {gather*} \frac {1}{20} x^{20} b^{5} B + \frac {5}{17} x^{17} b^{4} a B + \frac {1}{17} x^{17} b^{5} A + \frac {5}{7} x^{14} b^{3} a^{2} B + \frac {5}{14} x^{14} b^{4} a A + \frac {10}{11} x^{11} b^{2} a^{3} B + \frac {10}{11} x^{11} b^{3} a^{2} A + \frac {5}{8} x^{8} b a^{4} B + \frac {5}{4} x^{8} b^{2} a^{3} A + \frac {1}{5} x^{5} a^{5} B + x^{5} b a^{4} A + \frac {1}{2} x^{2} a^{5} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 124, normalized size = 1.06 \begin {gather*} \frac {1}{20} \, B b^{5} x^{20} + \frac {5}{17} \, B a b^{4} x^{17} + \frac {1}{17} \, A b^{5} x^{17} + \frac {5}{7} \, B a^{2} b^{3} x^{14} + \frac {5}{14} \, A a b^{4} x^{14} + \frac {10}{11} \, B a^{3} b^{2} x^{11} + \frac {10}{11} \, A a^{2} b^{3} x^{11} + \frac {5}{8} \, B a^{4} b x^{8} + \frac {5}{4} \, A a^{3} b^{2} x^{8} + \frac {1}{5} \, B a^{5} x^{5} + A a^{4} b x^{5} + \frac {1}{2} \, A a^{5} x^{2} \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^{20}}{20}+\frac {\left (b^{5} A +5 a \,b^{4} B \right ) x^{17}}{17}+\frac {\left (5 a \,b^{4} A +10 a^{2} b^{3} B \right ) x^{14}}{14}+\frac {\left (10 a^{2} b^{3} A +10 a^{3} b^{2} B \right ) x^{11}}{11}+\frac {A \,a^{5} x^{2}}{2}+\frac {\left (10 a^{3} b^{2} A +5 a^{4} b B \right ) x^{8}}{8}+\frac {\left (5 a^{4} b A +a^{5} B \right ) x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 119, normalized size = 1.02 \begin {gather*} \frac {1}{20} \, B b^{5} x^{20} + \frac {1}{17} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{17} + \frac {5}{14} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{14} + \frac {10}{11} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{11} + \frac {5}{8} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{8} + \frac {1}{2} \, A a^{5} x^{2} + \frac {1}{5} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 106, normalized size = 0.91 \begin {gather*} x^5\,\left (\frac {B\,a^5}{5}+A\,b\,a^4\right )+x^{17}\,\left (\frac {A\,b^5}{17}+\frac {5\,B\,a\,b^4}{17}\right )+\frac {A\,a^5\,x^2}{2}+\frac {B\,b^5\,x^{20}}{20}+\frac {10\,a^2\,b^2\,x^{11}\,\left (A\,b+B\,a\right )}{11}+\frac {5\,a^3\,b\,x^8\,\left (2\,A\,b+B\,a\right )}{8}+\frac {5\,a\,b^3\,x^{14}\,\left (A\,b+2\,B\,a\right )}{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 134, normalized size = 1.15 \begin {gather*} \frac {A a^{5} x^{2}}{2} + \frac {B b^{5} x^{20}}{20} + x^{17} \left (\frac {A b^{5}}{17} + \frac {5 B a b^{4}}{17}\right ) + x^{14} \left (\frac {5 A a b^{4}}{14} + \frac {5 B a^{2} b^{3}}{7}\right ) + x^{11} \left (\frac {10 A a^{2} b^{3}}{11} + \frac {10 B a^{3} b^{2}}{11}\right ) + x^{8} \left (\frac {5 A a^{3} b^{2}}{4} + \frac {5 B a^{4} b}{8}\right ) + x^{5} \left (A a^{4} b + \frac {B a^{5}}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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