Optimal. Leaf size=41 \[ -\frac {a^3}{x}+\frac {3}{2} a^2 b x^2+\frac {3}{5} a b^2 x^5+\frac {b^3 x^8}{8} \]
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Rubi [A] time = 0.01, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \frac {3}{2} a^2 b x^2-\frac {a^3}{x}+\frac {3}{5} a b^2 x^5+\frac {b^3 x^8}{8} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^2} \, dx &=\int \left (\frac {a^3}{x^2}+3 a^2 b x+3 a b^2 x^4+b^3 x^7\right ) \, dx\\ &=-\frac {a^3}{x}+\frac {3}{2} a^2 b x^2+\frac {3}{5} a b^2 x^5+\frac {b^3 x^8}{8}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 41, normalized size = 1.00 \[ -\frac {a^3}{x}+\frac {3}{2} a^2 b x^2+\frac {3}{5} a b^2 x^5+\frac {b^3 x^8}{8} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 37, normalized size = 0.90 \[ \frac {5 \, b^{3} x^{9} + 24 \, a b^{2} x^{6} + 60 \, a^{2} b x^{3} - 40 \, a^{3}}{40 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 35, normalized size = 0.85 \[ \frac {1}{8} \, b^{3} x^{8} + \frac {3}{5} \, a b^{2} x^{5} + \frac {3}{2} \, a^{2} b x^{2} - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.88 \[ \frac {b^{3} x^{8}}{8}+\frac {3 a \,b^{2} x^{5}}{5}+\frac {3 a^{2} b \,x^{2}}{2}-\frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 35, normalized size = 0.85 \[ \frac {1}{8} \, b^{3} x^{8} + \frac {3}{5} \, a b^{2} x^{5} + \frac {3}{2} \, a^{2} b x^{2} - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.85 \[ \frac {b^3\,x^8}{8}-\frac {a^3}{x}+\frac {3\,a^2\,b\,x^2}{2}+\frac {3\,a\,b^2\,x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 36, normalized size = 0.88 \[ - \frac {a^{3}}{x} + \frac {3 a^{2} b x^{2}}{2} + \frac {3 a b^{2} x^{5}}{5} + \frac {b^{3} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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