Optimal. Leaf size=39 \[ -\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4} \]
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Rubi [A] time = 0.01, antiderivative size = 39, 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} \[ -\frac {3 a^2 b}{2 x^2}-\frac {a^3}{5 x^5}+3 a b^2 x+\frac {b^3 x^4}{4} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^3}{x^6} \, dx &=\int \left (3 a b^2+\frac {a^3}{x^6}+\frac {3 a^2 b}{x^3}+b^3 x^3\right ) \, dx\\ &=-\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 39, normalized size = 1.00 \[ -\frac {a^3}{5 x^5}-\frac {3 a^2 b}{2 x^2}+3 a b^2 x+\frac {b^3 x^4}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 37, normalized size = 0.95 \[ \frac {5 \, b^{3} x^{9} + 60 \, a b^{2} x^{6} - 30 \, a^{2} b x^{3} - 4 \, a^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 36, normalized size = 0.92 \[ \frac {1}{4} \, b^{3} x^{4} + 3 \, a b^{2} x - \frac {15 \, a^{2} b x^{3} + 2 \, a^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 34, normalized size = 0.87 \[ \frac {b^{3} x^{4}}{4}+3 a \,b^{2} x -\frac {3 a^{2} b}{2 x^{2}}-\frac {a^{3}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 36, normalized size = 0.92 \[ \frac {1}{4} \, b^{3} x^{4} + 3 \, a b^{2} x - \frac {15 \, a^{2} b x^{3} + 2 \, a^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 36, normalized size = 0.92 \[ \frac {b^3\,x^4}{4}-\frac {\frac {a^3}{5}+\frac {3\,b\,a^2\,x^3}{2}}{x^5}+3\,a\,b^2\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 37, normalized size = 0.95 \[ 3 a b^{2} x + \frac {b^{3} x^{4}}{4} + \frac {- 2 a^{3} - 15 a^{2} b x^{3}}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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