Optimal. Leaf size=63 \[ \frac {2}{5} a^2 A x^{5/2}+\frac {2}{17} b x^{17/2} (2 a B+A b)+\frac {2}{11} a x^{11/2} (a B+2 A b)+\frac {2}{23} b^2 B x^{23/2} \]
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Rubi [A] time = 0.03, antiderivative size = 63, 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} \[ \frac {2}{5} a^2 A x^{5/2}+\frac {2}{17} b x^{17/2} (2 a B+A b)+\frac {2}{11} a x^{11/2} (a B+2 A b)+\frac {2}{23} b^2 B x^{23/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int x^{3/2} \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\int \left (a^2 A x^{3/2}+a (2 A b+a B) x^{9/2}+b (A b+2 a B) x^{15/2}+b^2 B x^{21/2}\right ) \, dx\\ &=\frac {2}{5} a^2 A x^{5/2}+\frac {2}{11} a (2 A b+a B) x^{11/2}+\frac {2}{17} b (A b+2 a B) x^{17/2}+\frac {2}{23} b^2 B x^{23/2}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 53, normalized size = 0.84 \[ \frac {2 x^{5/2} \left (4301 a^2 A+1265 b x^6 (2 a B+A b)+1955 a x^3 (a B+2 A b)+935 b^2 B x^9\right )}{21505} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.89, size = 56, normalized size = 0.89 \[ \frac {2}{21505} \, {\left (935 \, B b^{2} x^{11} + 1265 \, {\left (2 \, B a b + A b^{2}\right )} x^{8} + 1955 \, {\left (B a^{2} + 2 \, A a b\right )} x^{5} + 4301 \, A a^{2} x^{2}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 53, normalized size = 0.84 \[ \frac {2}{23} \, B b^{2} x^{\frac {23}{2}} + \frac {4}{17} \, B a b x^{\frac {17}{2}} + \frac {2}{17} \, A b^{2} x^{\frac {17}{2}} + \frac {2}{11} \, B a^{2} x^{\frac {11}{2}} + \frac {4}{11} \, A a b x^{\frac {11}{2}} + \frac {2}{5} \, A a^{2} x^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 56, normalized size = 0.89 \[ \frac {2 \left (935 b^{2} B \,x^{9}+1265 A \,b^{2} x^{6}+2530 B a b \,x^{6}+3910 A a b \,x^{3}+1955 B \,a^{2} x^{3}+4301 a^{2} A \right ) x^{\frac {5}{2}}}{21505} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 51, normalized size = 0.81 \[ \frac {2}{23} \, B b^{2} x^{\frac {23}{2}} + \frac {2}{17} \, {\left (2 \, B a b + A b^{2}\right )} x^{\frac {17}{2}} + \frac {2}{11} \, {\left (B a^{2} + 2 \, A a b\right )} x^{\frac {11}{2}} + \frac {2}{5} \, A a^{2} x^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 51, normalized size = 0.81 \[ x^{11/2}\,\left (\frac {2\,B\,a^2}{11}+\frac {4\,A\,b\,a}{11}\right )+x^{17/2}\,\left (\frac {2\,A\,b^2}{17}+\frac {4\,B\,a\,b}{17}\right )+\frac {2\,A\,a^2\,x^{5/2}}{5}+\frac {2\,B\,b^2\,x^{23/2}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.96, size = 80, normalized size = 1.27 \[ \frac {2 A a^{2} x^{\frac {5}{2}}}{5} + \frac {4 A a b x^{\frac {11}{2}}}{11} + \frac {2 A b^{2} x^{\frac {17}{2}}}{17} + \frac {2 B a^{2} x^{\frac {11}{2}}}{11} + \frac {4 B a b x^{\frac {17}{2}}}{17} + \frac {2 B b^{2} x^{\frac {23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
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