Optimal. Leaf size=85 \[ \frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
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Rubi [A] time = 0.041957, antiderivative size = 85, normalized size of antiderivative = 1., 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} \[ \frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^{3/2} \left (a+b x^3\right )^3 \left (A+B x^3\right ) \, dx &=\int \left (a^3 A x^{3/2}+a^2 (3 A b+a B) x^{9/2}+3 a b (A b+a B) x^{15/2}+b^2 (A b+3 a B) x^{21/2}+b^3 B x^{27/2}\right ) \, dx\\ &=\frac{2}{5} a^3 A x^{5/2}+\frac{2}{11} a^2 (3 A b+a B) x^{11/2}+\frac{6}{17} a b (A b+a B) x^{17/2}+\frac{2}{23} b^2 (A b+3 a B) x^{23/2}+\frac{2}{29} b^3 B x^{29/2}\\ \end{align*}
Mathematica [A] time = 0.040925, size = 85, normalized size = 1. \[ \frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 80, normalized size = 0.9 \begin{align*}{\frac{43010\,B{b}^{3}{x}^{12}+54230\,{x}^{9}A{b}^{3}+162690\,{x}^{9}Ba{b}^{2}+220110\,{x}^{6}Aa{b}^{2}+220110\,{x}^{6}B{a}^{2}b+340170\,{x}^{3}A{a}^{2}b+113390\,{x}^{3}B{a}^{3}+249458\,A{a}^{3}}{623645}{x}^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936533, size = 99, normalized size = 1.16 \begin{align*} \frac{2}{29} \, B b^{3} x^{\frac{29}{2}} + \frac{2}{23} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac{23}{2}} + \frac{6}{17} \,{\left (B a^{2} b + A a b^{2}\right )} x^{\frac{17}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} + \frac{2}{11} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac{11}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73349, size = 208, normalized size = 2.45 \begin{align*} \frac{2}{623645} \,{\left (21505 \, B b^{3} x^{14} + 27115 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{11} + 110055 \,{\left (B a^{2} b + A a b^{2}\right )} x^{8} + 124729 \, A a^{3} x^{2} + 56695 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{5}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 45.0458, size = 114, normalized size = 1.34 \begin{align*} \frac{2 A a^{3} x^{\frac{5}{2}}}{5} + \frac{6 A a^{2} b x^{\frac{11}{2}}}{11} + \frac{6 A a b^{2} x^{\frac{17}{2}}}{17} + \frac{2 A b^{3} x^{\frac{23}{2}}}{23} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{6 B a^{2} b x^{\frac{17}{2}}}{17} + \frac{6 B a b^{2} x^{\frac{23}{2}}}{23} + \frac{2 B b^{3} x^{\frac{29}{2}}}{29} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1227, size = 104, normalized size = 1.22 \begin{align*} \frac{2}{29} \, B b^{3} x^{\frac{29}{2}} + \frac{6}{23} \, B a b^{2} x^{\frac{23}{2}} + \frac{2}{23} \, A b^{3} x^{\frac{23}{2}} + \frac{6}{17} \, B a^{2} b x^{\frac{17}{2}} + \frac{6}{17} \, A a b^{2} x^{\frac{17}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{6}{11} \, A a^{2} b x^{\frac{11}{2}} + \frac{2}{5} \, A a^{3} x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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