Optimal. Leaf size=61 \[ 2 a^2 A \sqrt {x}+\frac {2}{13} b x^{13/2} (2 a B+A b)+\frac {2}{7} a x^{7/2} (a B+2 A b)+\frac {2}{19} b^2 B x^{19/2} \]
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Rubi [A] time = 0.03, antiderivative size = 61, normalized size of antiderivative = 1.00, 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} \[ 2 a^2 A \sqrt {x}+\frac {2}{13} b x^{13/2} (2 a B+A b)+\frac {2}{7} a x^{7/2} (a B+2 A b)+\frac {2}{19} b^2 B x^{19/2} \]
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 )}{\sqrt {x}} \, dx &=\int \left (\frac {a^2 A}{\sqrt {x}}+a (2 A b+a B) x^{5/2}+b (A b+2 a B) x^{11/2}+b^2 B x^{17/2}\right ) \, dx\\ &=2 a^2 A \sqrt {x}+\frac {2}{7} a (2 A b+a B) x^{7/2}+\frac {2}{13} b (A b+2 a B) x^{13/2}+\frac {2}{19} b^2 B x^{19/2}\\ \end {align*}
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Mathematica [A] time = 0.07, size = 53, normalized size = 0.87 \[ \frac {2 \sqrt {x} \left (1729 a^2 A+133 b x^6 (2 a B+A b)+247 a x^3 (a B+2 A b)+91 b^2 B x^9\right )}{1729} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 53, normalized size = 0.87 \[ \frac {2}{1729} \, {\left (91 \, B b^{2} x^{9} + 133 \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + 247 \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + 1729 \, A a^{2}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 53, normalized size = 0.87 \[ \frac {2}{19} \, B b^{2} x^{\frac {19}{2}} + \frac {4}{13} \, B a b x^{\frac {13}{2}} + \frac {2}{13} \, A b^{2} x^{\frac {13}{2}} + \frac {2}{7} \, B a^{2} x^{\frac {7}{2}} + \frac {4}{7} \, A a b x^{\frac {7}{2}} + 2 \, A a^{2} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 56, normalized size = 0.92 \[ \frac {2 \left (91 b^{2} B \,x^{9}+133 A \,b^{2} x^{6}+266 B a b \,x^{6}+494 A a b \,x^{3}+247 B \,a^{2} x^{3}+1729 a^{2} A \right ) \sqrt {x}}{1729} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 51, normalized size = 0.84 \[ \frac {2}{19} \, B b^{2} x^{\frac {19}{2}} + \frac {2}{13} \, {\left (2 \, B a b + A b^{2}\right )} x^{\frac {13}{2}} + \frac {2}{7} \, {\left (B a^{2} + 2 \, A a b\right )} x^{\frac {7}{2}} + 2 \, A a^{2} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 51, normalized size = 0.84 \[ x^{7/2}\,\left (\frac {2\,B\,a^2}{7}+\frac {4\,A\,b\,a}{7}\right )+x^{13/2}\,\left (\frac {2\,A\,b^2}{13}+\frac {4\,B\,a\,b}{13}\right )+2\,A\,a^2\,\sqrt {x}+\frac {2\,B\,b^2\,x^{19/2}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 9.22, size = 78, normalized size = 1.28 \[ 2 A a^{2} \sqrt {x} + \frac {4 A a b x^{\frac {7}{2}}}{7} + \frac {2 A b^{2} x^{\frac {13}{2}}}{13} + \frac {2 B a^{2} x^{\frac {7}{2}}}{7} + \frac {4 B a b x^{\frac {13}{2}}}{13} + \frac {2 B b^{2} x^{\frac {19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
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