Optimal. Leaf size=37 \[ \frac {2}{7} x^{7/2} (a B+A b)+2 a A \sqrt {x}+\frac {2}{13} b B x^{13/2} \]
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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} \[ \frac {2}{7} x^{7/2} (a B+A b)+2 a A \sqrt {x}+\frac {2}{13} b B x^{13/2} \]
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 )}{\sqrt {x}} \, dx &=\int \left (\frac {a A}{\sqrt {x}}+(A b+a B) x^{5/2}+b B x^{11/2}\right ) \, dx\\ &=2 a A \sqrt {x}+\frac {2}{7} (A b+a B) x^{7/2}+\frac {2}{13} b B x^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.07, size = 33, normalized size = 0.89 \[ \frac {2}{91} \sqrt {x} \left (13 x^3 (a B+A b)+91 a A+7 b B x^6\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 29, normalized size = 0.78 \[ \frac {2}{91} \, {\left (7 \, B b x^{6} + 13 \, {\left (B a + A b\right )} x^{3} + 91 \, A a\right )} \sqrt {x} \]
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 \[ \frac {2}{13} \, B b x^{\frac {13}{2}} + \frac {2}{7} \, B a x^{\frac {7}{2}} + \frac {2}{7} \, A b x^{\frac {7}{2}} + 2 \, A a \sqrt {x} \]
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 \[ \frac {2 \left (7 B b \,x^{6}+13 A b \,x^{3}+13 B a \,x^{3}+91 A a \right ) \sqrt {x}}{91} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 27, normalized size = 0.73 \[ \frac {2}{13} \, B b x^{\frac {13}{2}} + \frac {2}{7} \, {\left (B a + A b\right )} x^{\frac {7}{2}} + 2 \, A a \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.59, size = 31, normalized size = 0.84 \[ \frac {2\,\sqrt {x}\,\left (91\,A\,a+13\,A\,b\,x^3+13\,B\,a\,x^3+7\,B\,b\,x^6\right )}{91} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.30, size = 44, normalized size = 1.19 \[ 2 A a \sqrt {x} + \frac {2 A b x^{\frac {7}{2}}}{7} + \frac {2 B a x^{\frac {7}{2}}}{7} + \frac {2 B b x^{\frac {13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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