Optimal. Leaf size=30 \[ -\frac {a^2}{8 x^8}-\frac {2 a b}{5 x^5}-\frac {b^2}{2 x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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} \[ -\frac {a^2}{8 x^8}-\frac {2 a b}{5 x^5}-\frac {b^2}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^2}{x^9} \, dx &=\int \left (\frac {a^2}{x^9}+\frac {2 a b}{x^6}+\frac {b^2}{x^3}\right ) \, dx\\ &=-\frac {a^2}{8 x^8}-\frac {2 a b}{5 x^5}-\frac {b^2}{2 x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ -\frac {a^2}{8 x^8}-\frac {2 a b}{5 x^5}-\frac {b^2}{2 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 26, normalized size = 0.87 \[ -\frac {20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 26, normalized size = 0.87 \[ -\frac {20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 0.83 \[ -\frac {b^{2}}{2 x^{2}}-\frac {2 a b}{5 x^{5}}-\frac {a^{2}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 26, normalized size = 0.87 \[ -\frac {20 \, b^{2} x^{6} + 16 \, a b x^{3} + 5 \, a^{2}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 26, normalized size = 0.87 \[ -\frac {\frac {a^2}{8}+\frac {2\,a\,b\,x^3}{5}+\frac {b^2\,x^6}{2}}{x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 27, normalized size = 0.90 \[ \frac {- 5 a^{2} - 16 a b x^{3} - 20 b^{2} x^{6}}{40 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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