Optimal. Leaf size=63 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2} \]
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Rubi [A] time = 0.0306103, antiderivative size = 63, 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} \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^{7/2} \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\int \left (a^2 A x^{7/2}+a (2 A b+a B) x^{13/2}+b (A b+2 a B) x^{19/2}+b^2 B x^{25/2}\right ) \, dx\\ &=\frac{2}{9} a^2 A x^{9/2}+\frac{2}{15} a (2 A b+a B) x^{15/2}+\frac{2}{21} b (A b+2 a B) x^{21/2}+\frac{2}{27} b^2 B x^{27/2}\\ \end{align*}
Mathematica [A] time = 0.030353, size = 53, normalized size = 0.84 \[ \frac{2}{945} x^{9/2} \left (105 a^2 A+45 b x^6 (2 a B+A b)+63 a x^3 (a B+2 A b)+35 b^2 B x^9\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 56, normalized size = 0.9 \begin{align*}{\frac{70\,B{b}^{2}{x}^{9}+90\,A{b}^{2}{x}^{6}+180\,B{x}^{6}ab+252\,aAb{x}^{3}+126\,B{x}^{3}{a}^{2}+210\,{a}^{2}A}{945}{x}^{{\frac{9}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.945678, size = 69, normalized size = 1.1 \begin{align*} \frac{2}{27} \, B b^{2} x^{\frac{27}{2}} + \frac{2}{21} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{21}{2}} + \frac{2}{15} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{15}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67165, size = 138, normalized size = 2.19 \begin{align*} \frac{2}{945} \,{\left (35 \, B b^{2} x^{13} + 45 \,{\left (2 \, B a b + A b^{2}\right )} x^{10} + 63 \,{\left (B a^{2} + 2 \, A a b\right )} x^{7} + 105 \, A a^{2} x^{4}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 51.8472, size = 80, normalized size = 1.27 \begin{align*} \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{15}{2}}}{15} + \frac{2 A b^{2} x^{\frac{21}{2}}}{21} + \frac{2 B a^{2} x^{\frac{15}{2}}}{15} + \frac{4 B a b x^{\frac{21}{2}}}{21} + \frac{2 B b^{2} x^{\frac{27}{2}}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07986, size = 72, normalized size = 1.14 \begin{align*} \frac{2}{27} \, B b^{2} x^{\frac{27}{2}} + \frac{4}{21} \, B a b x^{\frac{21}{2}} + \frac{2}{21} \, A b^{2} x^{\frac{21}{2}} + \frac{2}{15} \, B a^{2} x^{\frac{15}{2}} + \frac{4}{15} \, A a b x^{\frac{15}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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