Optimal. Leaf size=109 \[ a^5 A x+\frac {1}{4} a^4 x^4 (a B+5 A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+a^2 b^2 x^{10} (a B+A b)+\frac {1}{16} b^4 x^{16} (5 a B+A b)+\frac {5}{13} a b^3 x^{13} (2 a B+A b)+\frac {1}{19} b^5 B x^{19} \]
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Rubi [A] time = 0.06, antiderivative size = 109, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {373} \begin {gather*} a^2 b^2 x^{10} (a B+A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+\frac {1}{4} a^4 x^4 (a B+5 A b)+a^5 A x+\frac {1}{16} b^4 x^{16} (5 a B+A b)+\frac {5}{13} a b^3 x^{13} (2 a B+A b)+\frac {1}{19} b^5 B x^{19} \end {gather*}
Antiderivative was successfully verified.
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Rule 373
Rubi steps
\begin {align*} \int \left (a+b x^3\right )^5 \left (A+B x^3\right ) \, dx &=\int \left (a^5 A+a^4 (5 A b+a B) x^3+5 a^3 b (2 A b+a B) x^6+10 a^2 b^2 (A b+a B) x^9+5 a b^3 (A b+2 a B) x^{12}+b^4 (A b+5 a B) x^{15}+b^5 B x^{18}\right ) \, dx\\ &=a^5 A x+\frac {1}{4} a^4 (5 A b+a B) x^4+\frac {5}{7} a^3 b (2 A b+a B) x^7+a^2 b^2 (A b+a B) x^{10}+\frac {5}{13} a b^3 (A b+2 a B) x^{13}+\frac {1}{16} b^4 (A b+5 a B) x^{16}+\frac {1}{19} b^5 B x^{19}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 109, normalized size = 1.00 \begin {gather*} a^5 A x+\frac {1}{4} a^4 x^4 (a B+5 A b)+\frac {5}{7} a^3 b x^7 (a B+2 A b)+a^2 b^2 x^{10} (a B+A b)+\frac {1}{16} b^4 x^{16} (5 a B+A b)+\frac {5}{13} a b^3 x^{13} (2 a B+A b)+\frac {1}{19} b^5 B x^{19} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \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 = 120, normalized size = 1.10 \begin {gather*} \frac {1}{19} x^{19} b^{5} B + \frac {5}{16} x^{16} b^{4} a B + \frac {1}{16} x^{16} b^{5} A + \frac {10}{13} x^{13} b^{3} a^{2} B + \frac {5}{13} x^{13} b^{4} a A + x^{10} b^{2} a^{3} B + x^{10} b^{3} a^{2} A + \frac {5}{7} x^{7} b a^{4} B + \frac {10}{7} x^{7} b^{2} a^{3} A + \frac {1}{4} x^{4} a^{5} B + \frac {5}{4} x^{4} b a^{4} A + x a^{5} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 120, normalized size = 1.10 \begin {gather*} \frac {1}{19} \, B b^{5} x^{19} + \frac {5}{16} \, B a b^{4} x^{16} + \frac {1}{16} \, A b^{5} x^{16} + \frac {10}{13} \, B a^{2} b^{3} x^{13} + \frac {5}{13} \, A a b^{4} x^{13} + B a^{3} b^{2} x^{10} + A a^{2} b^{3} x^{10} + \frac {5}{7} \, B a^{4} b x^{7} + \frac {10}{7} \, A a^{3} b^{2} x^{7} + \frac {1}{4} \, B a^{5} x^{4} + \frac {5}{4} \, A a^{4} b x^{4} + A a^{5} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 121, normalized size = 1.11 \begin {gather*} \frac {B \,b^{5} x^{19}}{19}+\frac {\left (b^{5} A +5 a \,b^{4} B \right ) x^{16}}{16}+\frac {\left (5 a \,b^{4} A +10 a^{2} b^{3} B \right ) x^{13}}{13}+\frac {\left (10 a^{2} b^{3} A +10 a^{3} b^{2} B \right ) x^{10}}{10}+A \,a^{5} x +\frac {\left (10 a^{3} b^{2} A +5 a^{4} b B \right ) x^{7}}{7}+\frac {\left (5 a^{4} b A +a^{5} B \right ) x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 115, normalized size = 1.06 \begin {gather*} \frac {1}{19} \, B b^{5} x^{19} + \frac {1}{16} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{16} + \frac {5}{13} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{13} + {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{10} + \frac {5}{7} \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{7} + A a^{5} x + \frac {1}{4} \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 103, normalized size = 0.94 \begin {gather*} x^4\,\left (\frac {B\,a^5}{4}+\frac {5\,A\,b\,a^4}{4}\right )+x^{16}\,\left (\frac {A\,b^5}{16}+\frac {5\,B\,a\,b^4}{16}\right )+\frac {B\,b^5\,x^{19}}{19}+A\,a^5\,x+a^2\,b^2\,x^{10}\,\left (A\,b+B\,a\right )+\frac {5\,a^3\,b\,x^7\,\left (2\,A\,b+B\,a\right )}{7}+\frac {5\,a\,b^3\,x^{13}\,\left (A\,b+2\,B\,a\right )}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 128, normalized size = 1.17 \begin {gather*} A a^{5} x + \frac {B b^{5} x^{19}}{19} + x^{16} \left (\frac {A b^{5}}{16} + \frac {5 B a b^{4}}{16}\right ) + x^{13} \left (\frac {5 A a b^{4}}{13} + \frac {10 B a^{2} b^{3}}{13}\right ) + x^{10} \left (A a^{2} b^{3} + B a^{3} b^{2}\right ) + x^{7} \left (\frac {10 A a^{3} b^{2}}{7} + \frac {5 B a^{4} b}{7}\right ) + x^{4} \left (\frac {5 A a^{4} b}{4} + \frac {B a^{5}}{4}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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