Optimal. Leaf size=39 \[ \frac {2}{11} x^{11/2} (a B+A b)+\frac {2}{5} a A x^{5/2}+\frac {2}{17} b B x^{17/2} \]
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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} \[ \frac {2}{11} x^{11/2} (a B+A b)+\frac {2}{5} a A x^{5/2}+\frac {2}{17} b B x^{17/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x^{3/2} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^{3/2}+(A b+a B) x^{9/2}+b B x^{15/2}\right ) \, dx\\ &=\frac {2}{5} a A x^{5/2}+\frac {2}{11} (A b+a B) x^{11/2}+\frac {2}{17} b B x^{17/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 0.85 \[ \frac {2}{935} x^{5/2} \left (85 x^3 (a B+A b)+187 a A+55 b B x^6\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 32, normalized size = 0.82 \[ \frac {2}{935} \, {\left (55 \, B b x^{8} + 85 \, {\left (B a + A b\right )} x^{5} + 187 \, A a x^{2}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 29, normalized size = 0.74 \[ \frac {2}{17} \, B b x^{\frac {17}{2}} + \frac {2}{11} \, B a x^{\frac {11}{2}} + \frac {2}{11} \, A b x^{\frac {11}{2}} + \frac {2}{5} \, A a x^{\frac {5}{2}} \]
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 \[ \frac {2 \left (55 B b \,x^{6}+85 A b \,x^{3}+85 B a \,x^{3}+187 A a \right ) x^{\frac {5}{2}}}{935} \]
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 \[ \frac {2}{17} \, B b x^{\frac {17}{2}} + \frac {2}{11} \, {\left (B a + A b\right )} x^{\frac {11}{2}} + \frac {2}{5} \, A a x^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 31, normalized size = 0.79 \[ \frac {2\,x^{5/2}\,\left (187\,A\,a+85\,A\,b\,x^3+85\,B\,a\,x^3+55\,B\,b\,x^6\right )}{935} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 6.74, size = 46, normalized size = 1.18 \[ \frac {2 A a x^{\frac {5}{2}}}{5} + \frac {2 A b x^{\frac {11}{2}}}{11} + \frac {2 B a x^{\frac {11}{2}}}{11} + \frac {2 B b x^{\frac {17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
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