Optimal. Leaf size=19 \[ -\frac {\left (a+b x^2\right )^4}{8 a x^8} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {264} \begin {gather*} -\frac {\left (a+b x^2\right )^4}{8 a x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^3}{x^9} \, dx &=-\frac {\left (a+b x^2\right )^4}{8 a x^8}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 43, normalized size = 2.26 \begin {gather*} -\frac {a^3}{8 x^8}-\frac {a^2 b}{2 x^6}-\frac {3 a b^2}{4 x^4}-\frac {b^3}{2 x^2} \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^2\right )^3}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.74, size = 35, normalized size = 1.84 \begin {gather*} -\frac {4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.04, size = 35, normalized size = 1.84 \begin {gather*} -\frac {4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 36, normalized size = 1.89 \begin {gather*} -\frac {b^{3}}{2 x^{2}}-\frac {3 a \,b^{2}}{4 x^{4}}-\frac {a^{2} b}{2 x^{6}}-\frac {a^{3}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.32, size = 35, normalized size = 1.84 \begin {gather*} -\frac {4 \, b^{3} x^{6} + 6 \, a b^{2} x^{4} + 4 \, a^{2} b x^{2} + a^{3}}{8 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 1.95 \begin {gather*} -\frac {\frac {a^3}{8}+\frac {a^2\,b\,x^2}{2}+\frac {3\,a\,b^2\,x^4}{4}+\frac {b^3\,x^6}{2}}{x^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.27, size = 37, normalized size = 1.95 \begin {gather*} \frac {- a^{3} - 4 a^{2} b x^{2} - 6 a b^{2} x^{4} - 4 b^{3} x^{6}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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