Optimal. Leaf size=39 \[ \frac {2}{13} x^{13/2} (a B+A b)+\frac {2}{7} a A x^{7/2}+\frac {2}{19} b B x^{19/2} \]
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Rubi [A] time = 0.02, antiderivative size = 39, 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 {2}{13} x^{13/2} (a B+A b)+\frac {2}{7} a A x^{7/2}+\frac {2}{19} b B x^{19/2} \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 ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^{5/2}+(A b+a B) x^{11/2}+b B x^{17/2}\right ) \, dx\\ &=\frac {2}{7} a A x^{7/2}+\frac {2}{13} (A b+a B) x^{13/2}+\frac {2}{19} b B x^{19/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.85 \begin {gather*} \frac {2 x^{7/2} \left (133 x^3 (a B+A b)+247 a A+91 b B x^6\right )}{1729} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 41, normalized size = 1.05 \begin {gather*} \frac {2 \left (247 a A x^{7/2}+133 a B x^{13/2}+133 A b x^{13/2}+91 b B x^{19/2}\right )}{1729} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 32, normalized size = 0.82 \begin {gather*} \frac {2}{1729} \, {\left (91 \, B b x^{9} + 133 \, {\left (B a + A b\right )} x^{6} + 247 \, A a x^{3}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.74 \begin {gather*} \frac {2}{19} \, B b x^{\frac {19}{2}} + \frac {2}{13} \, B a x^{\frac {13}{2}} + \frac {2}{13} \, A b x^{\frac {13}{2}} + \frac {2}{7} \, A a 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 = 32, normalized size = 0.82 \begin {gather*} \frac {2 \left (91 B b \,x^{6}+133 A b \,x^{3}+133 B a \,x^{3}+247 A a \right ) x^{\frac {7}{2}}}{1729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 27, normalized size = 0.69 \begin {gather*} \frac {2}{19} \, B b x^{\frac {19}{2}} + \frac {2}{13} \, {\left (B a + A b\right )} x^{\frac {13}{2}} + \frac {2}{7} \, A a x^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.56, size = 31, normalized size = 0.79 \begin {gather*} \frac {2\,x^{7/2}\,\left (247\,A\,a+133\,A\,b\,x^3+133\,B\,a\,x^3+91\,B\,b\,x^6\right )}{1729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 12.71, size = 46, normalized size = 1.18 \begin {gather*} \frac {2 A a x^{\frac {7}{2}}}{7} + \frac {2 A b x^{\frac {13}{2}}}{13} + \frac {2 B a x^{\frac {13}{2}}}{13} + \frac {2 B b x^{\frac {19}{2}}}{19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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