Optimal. Leaf size=83 \[ 2 a^3 A \sqrt {x}+\frac {2}{7} a^2 x^{7/2} (a B+3 A b)+\frac {2}{19} b^2 x^{19/2} (3 a B+A b)+\frac {6}{13} a b x^{13/2} (a B+A b)+\frac {2}{25} b^3 B x^{25/2} \]
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Rubi [A] time = 0.04, antiderivative size = 83, 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} \[ \frac {2}{7} a^2 x^{7/2} (a B+3 A b)+2 a^3 A \sqrt {x}+\frac {2}{19} b^2 x^{19/2} (3 a B+A b)+\frac {6}{13} a b x^{13/2} (a B+A b)+\frac {2}{25} b^3 B x^{25/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3 \left (A+B x^3\right )}{\sqrt {x}} \, dx &=\int \left (\frac {a^3 A}{\sqrt {x}}+a^2 (3 A b+a B) x^{5/2}+3 a b (A b+a B) x^{11/2}+b^2 (A b+3 a B) x^{17/2}+b^3 B x^{23/2}\right ) \, dx\\ &=2 a^3 A \sqrt {x}+\frac {2}{7} a^2 (3 A b+a B) x^{7/2}+\frac {6}{13} a b (A b+a B) x^{13/2}+\frac {2}{19} b^2 (A b+3 a B) x^{19/2}+\frac {2}{25} b^3 B x^{25/2}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 83, normalized size = 1.00 \[ 2 a^3 A \sqrt {x}+\frac {2}{7} a^2 x^{7/2} (a B+3 A b)+\frac {2}{19} b^2 x^{19/2} (3 a B+A b)+\frac {6}{13} a b x^{13/2} (a B+A b)+\frac {2}{25} b^3 B x^{25/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.45, size = 75, normalized size = 0.90 \[ \frac {2}{43225} \, {\left (1729 \, B b^{3} x^{12} + 2275 \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{9} + 9975 \, {\left (B a^{2} b + A a b^{2}\right )} x^{6} + 43225 \, A a^{3} + 6175 \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x^{3}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 77, normalized size = 0.93 \[ \frac {2}{25} \, B b^{3} x^{\frac {25}{2}} + \frac {6}{19} \, B a b^{2} x^{\frac {19}{2}} + \frac {2}{19} \, A b^{3} x^{\frac {19}{2}} + \frac {6}{13} \, B a^{2} b x^{\frac {13}{2}} + \frac {6}{13} \, A a b^{2} x^{\frac {13}{2}} + \frac {2}{7} \, B a^{3} x^{\frac {7}{2}} + \frac {6}{7} \, A a^{2} b x^{\frac {7}{2}} + 2 \, A a^{3} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 80, normalized size = 0.96 \[ \frac {2 \left (1729 B \,b^{3} x^{12}+2275 x^{9} A \,b^{3}+6825 x^{9} B a \,b^{2}+9975 x^{6} A a \,b^{2}+9975 x^{6} B \,a^{2} b +18525 x^{3} A \,a^{2} b +6175 B \,a^{3} x^{3}+43225 A \,a^{3}\right ) \sqrt {x}}{43225} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 73, normalized size = 0.88 \[ \frac {2}{25} \, B b^{3} x^{\frac {25}{2}} + \frac {2}{19} \, {\left (3 \, B a b^{2} + A b^{3}\right )} x^{\frac {19}{2}} + \frac {6}{13} \, {\left (B a^{2} b + A a b^{2}\right )} x^{\frac {13}{2}} + 2 \, A a^{3} \sqrt {x} + \frac {2}{7} \, {\left (B a^{3} + 3 \, A a^{2} b\right )} x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 69, normalized size = 0.83 \[ x^{7/2}\,\left (\frac {2\,B\,a^3}{7}+\frac {6\,A\,b\,a^2}{7}\right )+x^{19/2}\,\left (\frac {2\,A\,b^3}{19}+\frac {6\,B\,a\,b^2}{19}\right )+2\,A\,a^3\,\sqrt {x}+\frac {2\,B\,b^3\,x^{25/2}}{25}+\frac {6\,a\,b\,x^{13/2}\,\left (A\,b+B\,a\right )}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.64, size = 112, normalized size = 1.35 \[ 2 A a^{3} \sqrt {x} + \frac {6 A a^{2} b x^{\frac {7}{2}}}{7} + \frac {6 A a b^{2} x^{\frac {13}{2}}}{13} + \frac {2 A b^{3} x^{\frac {19}{2}}}{19} + \frac {2 B a^{3} x^{\frac {7}{2}}}{7} + \frac {6 B a^{2} b x^{\frac {13}{2}}}{13} + \frac {6 B a b^{2} x^{\frac {19}{2}}}{19} + \frac {2 B b^{3} x^{\frac {25}{2}}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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