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 = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \begin {gather*} \frac {2}{5} x^{5/2} (a B+A b)-\frac {2 a A}{\sqrt {x}}+\frac {2}{11} b B x^{11/2} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 0.95 \begin {gather*} \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}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 35, normalized size = 0.95 \begin {gather*} \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}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 29, normalized size = 0.78 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.78 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 32, normalized size = 0.86 \begin {gather*} -\frac {2 \left (-5 B b \,x^{6}-11 A b \,x^{3}-11 B a \,x^{3}+55 A a \right )}{55 \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 27, normalized size = 0.73 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.60, size = 31, normalized size = 0.84 \begin {gather*} \frac {22\,A\,b\,x^3-110\,A\,a+22\,B\,a\,x^3+10\,B\,b\,x^6}{55\,\sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.77, size = 44, normalized size = 1.19 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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