Optimal. Leaf size=61 \[ -\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2} \]
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Rubi [A] time = 0.0303508, antiderivative size = 61, 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} \[ -\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^{3/2}} \, dx &=\int \left (\frac{a^2 A}{x^{3/2}}+a (2 A b+a B) x^{3/2}+b (A b+2 a B) x^{9/2}+b^2 B x^{15/2}\right ) \, dx\\ &=-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{5} a (2 A b+a B) x^{5/2}+\frac{2}{11} b (A b+2 a B) x^{11/2}+\frac{2}{17} b^2 B x^{17/2}\\ \end{align*}
Mathematica [A] time = 0.0189261, size = 60, normalized size = 0.98 \[ \frac{-374 a^2 \left (5 A-B x^3\right )+68 a b x^3 \left (11 A+5 B x^3\right )+10 b^2 x^6 \left (17 A+11 B x^3\right )}{935 \sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 56, normalized size = 0.9 \begin{align*} -{\frac{-110\,B{b}^{2}{x}^{9}-170\,A{b}^{2}{x}^{6}-340\,B{x}^{6}ab-748\,aAb{x}^{3}-374\,B{x}^{3}{a}^{2}+1870\,{a}^{2}A}{935}{\frac{1}{\sqrt{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940555, size = 69, normalized size = 1.13 \begin{align*} \frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{2}{11} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{11}{2}} + \frac{2}{5} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{5}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68896, size = 131, normalized size = 2.15 \begin{align*} \frac{2 \,{\left (55 \, B b^{2} x^{9} + 85 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 187 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 935 \, A a^{2}\right )}}{935 \, \sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 7.95219, size = 78, normalized size = 1.28 \begin{align*} - \frac{2 A a^{2}}{\sqrt{x}} + \frac{4 A a b x^{\frac{5}{2}}}{5} + \frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} x^{\frac{5}{2}}}{5} + \frac{4 B a b x^{\frac{11}{2}}}{11} + \frac{2 B b^{2} x^{\frac{17}{2}}}{17} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1013, size = 72, normalized size = 1.18 \begin{align*} \frac{2}{17} \, B b^{2} x^{\frac{17}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{2}{5} \, B a^{2} x^{\frac{5}{2}} + \frac{4}{5} \, A a b x^{\frac{5}{2}} - \frac{2 \, A a^{2}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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