Optimal. Leaf size=42 \[ \frac {\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac {B \left (a+b x^3\right )^4}{12 b^2} \]
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Rubi [A] time = 0.07, antiderivative size = 42, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {444, 43} \begin {gather*} \frac {\left (a+b x^3\right )^3 (A b-a B)}{9 b^2}+\frac {B \left (a+b x^3\right )^4}{12 b^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 444
Rubi steps
\begin {align*} \int x^2 \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int (a+b x)^2 (A+B x) \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {(A b-a B) (a+b x)^2}{b}+\frac {B (a+b x)^3}{b}\right ) \, dx,x,x^3\right )\\ &=\frac {(A b-a B) \left (a+b x^3\right )^3}{9 b^2}+\frac {B \left (a+b x^3\right )^4}{12 b^2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 51, normalized size = 1.21 \begin {gather*} \frac {1}{36} x^3 \left (12 a^2 A+4 b x^6 (2 a B+A b)+6 a x^3 (a B+2 A b)+3 b^2 B x^9\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.03, size = 53, normalized size = 1.26 \begin {gather*} \frac {1}{12} x^{12} b^{2} B + \frac {2}{9} x^{9} b a B + \frac {1}{9} x^{9} b^{2} A + \frac {1}{6} x^{6} a^{2} B + \frac {1}{3} x^{6} b a A + \frac {1}{3} x^{3} a^{2} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 53, normalized size = 1.26 \begin {gather*} \frac {1}{12} \, B b^{2} x^{12} + \frac {2}{9} \, B a b x^{9} + \frac {1}{9} \, A b^{2} x^{9} + \frac {1}{6} \, B a^{2} x^{6} + \frac {1}{3} \, A a b x^{6} + \frac {1}{3} \, A a^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 52, normalized size = 1.24 \begin {gather*} \frac {B \,b^{2} x^{12}}{12}+\frac {\left (b^{2} A +2 a b B \right ) x^{9}}{9}+\frac {A \,a^{2} x^{3}}{3}+\frac {\left (2 a b A +a^{2} B \right ) x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 51, normalized size = 1.21 \begin {gather*} \frac {1}{12} \, B b^{2} x^{12} + \frac {1}{9} \, {\left (2 \, B a b + A b^{2}\right )} x^{9} + \frac {1}{6} \, {\left (B a^{2} + 2 \, A a b\right )} x^{6} + \frac {1}{3} \, A a^{2} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.38, size = 51, normalized size = 1.21 \begin {gather*} x^6\,\left (\frac {B\,a^2}{6}+\frac {A\,b\,a}{3}\right )+x^9\,\left (\frac {A\,b^2}{9}+\frac {2\,B\,a\,b}{9}\right )+\frac {A\,a^2\,x^3}{3}+\frac {B\,b^2\,x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 54, normalized size = 1.29 \begin {gather*} \frac {A a^{2} x^{3}}{3} + \frac {B b^{2} x^{12}}{12} + x^{9} \left (\frac {A b^{2}}{9} + \frac {2 B a b}{9}\right ) + x^{6} \left (\frac {A a b}{3} + \frac {B a^{2}}{6}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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