Optimal. Leaf size=63 \[ \frac{2}{5} a^2 A x^{5/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{23} b^2 B x^{23/2} \]
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Rubi [A] time = 0.0299877, 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} \[ \frac{2}{5} a^2 A x^{5/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{23} b^2 B x^{23/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^{3/2} \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\int \left (a^2 A x^{3/2}+a (2 A b+a B) x^{9/2}+b (A b+2 a B) x^{15/2}+b^2 B x^{21/2}\right ) \, dx\\ &=\frac{2}{5} a^2 A x^{5/2}+\frac{2}{11} a (2 A b+a B) x^{11/2}+\frac{2}{17} b (A b+2 a B) x^{17/2}+\frac{2}{23} b^2 B x^{23/2}\\ \end{align*}
Mathematica [A] time = 0.027907, size = 53, normalized size = 0.84 \[ \frac{2 x^{5/2} \left (4301 a^2 A+1265 b x^6 (2 a B+A b)+1955 a x^3 (a B+2 A b)+935 b^2 B x^9\right )}{21505} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 56, normalized size = 0.9 \begin{align*}{\frac{1870\,B{b}^{2}{x}^{9}+2530\,A{b}^{2}{x}^{6}+5060\,B{x}^{6}ab+7820\,aAb{x}^{3}+3910\,B{x}^{3}{a}^{2}+8602\,{a}^{2}A}{21505}{x}^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937444, size = 69, normalized size = 1.1 \begin{align*} \frac{2}{23} \, B b^{2} x^{\frac{23}{2}} + \frac{2}{17} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{17}{2}} + \frac{2}{11} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{11}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63661, size = 147, normalized size = 2.33 \begin{align*} \frac{2}{21505} \,{\left (935 \, B b^{2} x^{11} + 1265 \,{\left (2 \, B a b + A b^{2}\right )} x^{8} + 1955 \,{\left (B a^{2} + 2 \, A a b\right )} x^{5} + 4301 \, A a^{2} x^{2}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 18.7176, size = 80, normalized size = 1.27 \begin{align*} \frac{2 A a^{2} x^{\frac{5}{2}}}{5} + \frac{4 A a b x^{\frac{11}{2}}}{11} + \frac{2 A b^{2} x^{\frac{17}{2}}}{17} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a b x^{\frac{17}{2}}}{17} + \frac{2 B b^{2} x^{\frac{23}{2}}}{23} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12972, size = 72, normalized size = 1.14 \begin{align*} \frac{2}{23} \, B b^{2} x^{\frac{23}{2}} + \frac{4}{17} \, B a b x^{\frac{17}{2}} + \frac{2}{17} \, A b^{2} x^{\frac{17}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a b x^{\frac{11}{2}} + \frac{2}{5} \, A a^{2} x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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