Optimal. Leaf size=37 \[ \frac{2}{5} x^{5/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{11} b B x^{11/2} \]
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Rubi [A] time = 0.0148993, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ \frac{2}{5} x^{5/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{11} b B x^{11/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^{3/2}} \, dx &=\int \left (\frac{a A}{x^{3/2}}+(A b+a B) x^{3/2}+b B x^{9/2}\right ) \, dx\\ &=-\frac{2 a A}{\sqrt{x}}+\frac{2}{5} (A b+a B) x^{5/2}+\frac{2}{11} b B x^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0099154, size = 35, normalized size = 0.95 \[ \frac{2 \left (-55 a A+11 a B x^3+11 A b x^3+5 b B x^6\right )}{55 \sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 32, normalized size = 0.9 \begin{align*} -{\frac{-10\,bB{x}^{6}-22\,A{x}^{3}b-22\,B{x}^{3}a+110\,Aa}{55}{\frac{1}{\sqrt{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.947561, size = 36, normalized size = 0.97 \begin{align*} \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{5} \,{\left (B a + A b\right )} x^{\frac{5}{2}} - \frac{2 \, A a}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70209, size = 76, normalized size = 2.05 \begin{align*} \frac{2 \,{\left (5 \, B b x^{6} + 11 \,{\left (B a + A b\right )} x^{3} - 55 \, A a\right )}}{55 \, \sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.52094, size = 44, normalized size = 1.19 \begin{align*} - \frac{2 A a}{\sqrt{x}} + \frac{2 A b x^{\frac{5}{2}}}{5} + \frac{2 B a x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{11}{2}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09866, size = 39, normalized size = 1.05 \begin{align*} \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} - \frac{2 \, A a}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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