Optimal. Leaf size=36 \[ a^3 \log (x)+a^2 b x^3+\frac {1}{2} a b^2 x^6+\frac {b^3 x^9}{9} \]
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Rubi [A] time = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ a^2 b x^3+a^3 \log (x)+\frac {1}{2} a b^2 x^6+\frac {b^3 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (3 a^2 b+\frac {a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx,x,x^3\right )\\ &=a^2 b x^3+\frac {1}{2} a b^2 x^6+\frac {b^3 x^9}{9}+a^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 36, normalized size = 1.00 \[ a^3 \log (x)+a^2 b x^3+\frac {1}{2} a b^2 x^6+\frac {b^3 x^9}{9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 32, normalized size = 0.89 \[ \frac {1}{9} \, b^{3} x^{9} + \frac {1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 33, normalized size = 0.92 \[ \frac {1}{9} \, b^{3} x^{9} + \frac {1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.92 \[ \frac {b^{3} x^{9}}{9}+\frac {a \,b^{2} x^{6}}{2}+a^{2} b \,x^{3}+a^{3} \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 35, normalized size = 0.97 \[ \frac {1}{9} \, b^{3} x^{9} + \frac {1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + \frac {1}{3} \, a^{3} \log \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 32, normalized size = 0.89 \[ a^3\,\ln \relax (x)+\frac {b^3\,x^9}{9}+a^2\,b\,x^3+\frac {a\,b^2\,x^6}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 32, normalized size = 0.89 \[ a^{3} \log {\relax (x )} + a^{2} b x^{3} + \frac {a b^{2} x^{6}}{2} + \frac {b^{3} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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