Optimal. Leaf size=63 \[ \frac {2}{7} a^2 A x^{7/2}+\frac {2}{19} b x^{19/2} (2 a B+A b)+\frac {2}{13} a x^{13/2} (a B+2 A b)+\frac {2}{25} b^2 B x^{25/2} \]
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Rubi [A] time = 0.03, antiderivative size = 63, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {448} \begin {gather*} \frac {2}{7} a^2 A x^{7/2}+\frac {2}{19} b x^{19/2} (2 a B+A b)+\frac {2}{13} a x^{13/2} (a B+2 A b)+\frac {2}{25} b^2 B x^{25/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x^{5/2} \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\int \left (a^2 A x^{5/2}+a (2 A b+a B) x^{11/2}+b (A b+2 a B) x^{17/2}+b^2 B x^{23/2}\right ) \, dx\\ &=\frac {2}{7} a^2 A x^{7/2}+\frac {2}{13} a (2 A b+a B) x^{13/2}+\frac {2}{19} b (A b+2 a B) x^{19/2}+\frac {2}{25} b^2 B x^{25/2}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 63, normalized size = 1.00 \begin {gather*} \frac {2}{7} a^2 A x^{7/2}+\frac {2}{19} b x^{19/2} (2 a B+A b)+\frac {2}{13} a x^{13/2} (a B+2 A b)+\frac {2}{25} b^2 B x^{25/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.03, size = 69, normalized size = 1.10 \begin {gather*} \frac {2 \left (6175 a^2 A x^{7/2}+3325 a^2 B x^{13/2}+6650 a A b x^{13/2}+4550 a b B x^{19/2}+2275 A b^2 x^{19/2}+1729 b^2 B x^{25/2}\right )}{43225} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 56, normalized size = 0.89 \begin {gather*} \frac {2}{43225} \, {\left (1729 \, B b^{2} x^{12} + 2275 \, {\left (2 \, B a b + A b^{2}\right )} x^{9} + 3325 \, {\left (B a^{2} + 2 \, A a b\right )} x^{6} + 6175 \, A a^{2} x^{3}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 53, normalized size = 0.84 \begin {gather*} \frac {2}{25} \, B b^{2} x^{\frac {25}{2}} + \frac {4}{19} \, B a b x^{\frac {19}{2}} + \frac {2}{19} \, A b^{2} x^{\frac {19}{2}} + \frac {2}{13} \, B a^{2} x^{\frac {13}{2}} + \frac {4}{13} \, A a b x^{\frac {13}{2}} + \frac {2}{7} \, A a^{2} x^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 56, normalized size = 0.89 \begin {gather*} \frac {2 \left (1729 b^{2} B \,x^{9}+2275 A \,b^{2} x^{6}+4550 B a b \,x^{6}+6650 A a b \,x^{3}+3325 B \,a^{2} x^{3}+6175 a^{2} A \right ) x^{\frac {7}{2}}}{43225} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 51, normalized size = 0.81 \begin {gather*} \frac {2}{25} \, B b^{2} x^{\frac {25}{2}} + \frac {2}{19} \, {\left (2 \, B a b + A b^{2}\right )} x^{\frac {19}{2}} + \frac {2}{13} \, {\left (B a^{2} + 2 \, A a b\right )} x^{\frac {13}{2}} + \frac {2}{7} \, A a^{2} x^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 51, normalized size = 0.81 \begin {gather*} x^{13/2}\,\left (\frac {2\,B\,a^2}{13}+\frac {4\,A\,b\,a}{13}\right )+x^{19/2}\,\left (\frac {2\,A\,b^2}{19}+\frac {4\,B\,a\,b}{19}\right )+\frac {2\,A\,a^2\,x^{7/2}}{7}+\frac {2\,B\,b^2\,x^{25/2}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 29.39, size = 80, normalized size = 1.27 \begin {gather*} \frac {2 A a^{2} x^{\frac {7}{2}}}{7} + \frac {4 A a b x^{\frac {13}{2}}}{13} + \frac {2 A b^{2} x^{\frac {19}{2}}}{19} + \frac {2 B a^{2} x^{\frac {13}{2}}}{13} + \frac {4 B a b x^{\frac {19}{2}}}{19} + \frac {2 B b^{2} x^{\frac {25}{2}}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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