Optimal. Leaf size=39 \[ \frac {2}{15} x^{15/2} (a B+A b)+\frac {2}{9} a A x^{9/2}+\frac {2}{21} b B x^{21/2} \]
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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}{15} x^{15/2} (a B+A b)+\frac {2}{9} a A x^{9/2}+\frac {2}{21} b B x^{21/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x^{7/2} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^{7/2}+(A b+a B) x^{13/2}+b B x^{19/2}\right ) \, dx\\ &=\frac {2}{9} a A x^{9/2}+\frac {2}{15} (A b+a B) x^{15/2}+\frac {2}{21} b B x^{21/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.85 \begin {gather*} \frac {2}{315} x^{9/2} \left (21 x^3 (a B+A b)+35 a A+15 b B x^6\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 35, normalized size = 0.90 \begin {gather*} \frac {2}{315} x^{9/2} \left (35 a A+21 a B x^3+21 A b x^3+15 b B x^6\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 32, normalized size = 0.82 \begin {gather*} \frac {2}{315} \, {\left (15 \, B b x^{10} + 21 \, {\left (B a + A b\right )} x^{7} + 35 \, A a x^{4}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 29, normalized size = 0.74 \begin {gather*} \frac {2}{21} \, B b x^{\frac {21}{2}} + \frac {2}{15} \, B a x^{\frac {15}{2}} + \frac {2}{15} \, A b x^{\frac {15}{2}} + \frac {2}{9} \, A a x^{\frac {9}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 32, normalized size = 0.82 \begin {gather*} \frac {2 \left (15 B b \,x^{6}+21 A b \,x^{3}+21 B a \,x^{3}+35 A a \right ) x^{\frac {9}{2}}}{315} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 27, normalized size = 0.69 \begin {gather*} \frac {2}{21} \, B b x^{\frac {21}{2}} + \frac {2}{15} \, {\left (B a + A b\right )} x^{\frac {15}{2}} + \frac {2}{9} \, A a x^{\frac {9}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 31, normalized size = 0.79 \begin {gather*} \frac {2\,x^{9/2}\,\left (35\,A\,a+21\,A\,b\,x^3+21\,B\,a\,x^3+15\,B\,b\,x^6\right )}{315} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 20.86, size = 46, normalized size = 1.18 \begin {gather*} \frac {2 A a x^{\frac {9}{2}}}{9} + \frac {2 A b x^{\frac {15}{2}}}{15} + \frac {2 B a x^{\frac {15}{2}}}{15} + \frac {2 B b x^{\frac {21}{2}}}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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