Optimal. Leaf size=46 \[ a^2 A \log (x)+\frac {2}{3} a A b x^3+\frac {B \left (a+b x^3\right )^3}{9 b}+\frac {1}{6} A b^2 x^6 \]
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Rubi [A] time = 0.03, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {446, 80, 43} \begin {gather*} a^2 A \log (x)+\frac {2}{3} a A b x^3+\frac {B \left (a+b x^3\right )^3}{9 b}+\frac {1}{6} A b^2 x^6 \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 80
Rule 446
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^2 (A+B x)}{x} \, dx,x,x^3\right )\\ &=\frac {B \left (a+b x^3\right )^3}{9 b}+\frac {1}{3} A \operatorname {Subst}\left (\int \frac {(a+b x)^2}{x} \, dx,x,x^3\right )\\ &=\frac {B \left (a+b x^3\right )^3}{9 b}+\frac {1}{3} A \operatorname {Subst}\left (\int \left (2 a b+\frac {a^2}{x}+b^2 x\right ) \, dx,x,x^3\right )\\ &=\frac {2}{3} a A b x^3+\frac {1}{6} A b^2 x^6+\frac {B \left (a+b x^3\right )^3}{9 b}+a^2 A \log (x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 51, normalized size = 1.11 \begin {gather*} a^2 A \log (x)+\frac {1}{6} b x^6 (2 a B+A b)+\frac {1}{3} a x^3 (a B+2 A b)+\frac {1}{9} b^2 B x^9 \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.77, size = 49, normalized size = 1.07 \begin {gather*} \frac {1}{9} \, B b^{2} x^{9} + \frac {1}{6} \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + \frac {1}{3} \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + A a^{2} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 52, normalized size = 1.13 \begin {gather*} \frac {1}{9} \, B b^{2} x^{9} + \frac {1}{3} \, B a b x^{6} + \frac {1}{6} \, A b^{2} x^{6} + \frac {1}{3} \, B a^{2} x^{3} + \frac {2}{3} \, A a b x^{3} + A a^{2} \log \left ({\left | x \right |}\right ) \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 = 1.13 \begin {gather*} \frac {B \,b^{2} x^{9}}{9}+\frac {A \,b^{2} x^{6}}{6}+\frac {B a b \,x^{6}}{3}+\frac {2 A a b \,x^{3}}{3}+\frac {B \,a^{2} x^{3}}{3}+A \,a^{2} \ln \relax (x ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 52, normalized size = 1.13 \begin {gather*} \frac {1}{9} \, B b^{2} x^{9} + \frac {1}{6} \, {\left (2 \, B a b + A b^{2}\right )} x^{6} + \frac {1}{3} \, {\left (B a^{2} + 2 \, A a b\right )} x^{3} + \frac {1}{3} \, A a^{2} \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 1.07 \begin {gather*} x^3\,\left (\frac {B\,a^2}{3}+\frac {2\,A\,b\,a}{3}\right )+x^6\,\left (\frac {A\,b^2}{6}+\frac {B\,a\,b}{3}\right )+\frac {B\,b^2\,x^9}{9}+A\,a^2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 53, normalized size = 1.15 \begin {gather*} A a^{2} \log {\relax (x )} + \frac {B b^{2} x^{9}}{9} + x^{6} \left (\frac {A b^{2}}{6} + \frac {B a b}{3}\right ) + x^{3} \left (\frac {2 A a b}{3} + \frac {B a^{2}}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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