Optimal. Leaf size=30 \[ -\frac {a^2}{8 x^8}-\frac {a b}{3 x^6}-\frac {b^2}{4 x^4} \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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} \begin {gather*} -\frac {a^2}{8 x^8}-\frac {a b}{3 x^6}-\frac {b^2}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^2}{x^9} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^2}{x^5} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (\frac {a^2}{x^5}+\frac {2 a b}{x^4}+\frac {b^2}{x^3}\right ) \, dx,x,x^2\right )\\ &=-\frac {a^2}{8 x^8}-\frac {a b}{3 x^6}-\frac {b^2}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{8 x^8}-\frac {a b}{3 x^6}-\frac {b^2}{4 x^4} \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 )^2}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.13, size = 26, normalized size = 0.87 \begin {gather*} -\frac {6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 26, normalized size = 0.87 \begin {gather*} -\frac {6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end {gather*}
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 \begin {gather*} -\frac {b^{2}}{4 x^{4}}-\frac {a b}{3 x^{6}}-\frac {a^{2}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 26, normalized size = 0.87 \begin {gather*} -\frac {6 \, b^{2} x^{4} + 8 \, a b x^{2} + 3 \, a^{2}}{24 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 0.87 \begin {gather*} -\frac {\frac {a^2}{8}+\frac {a\,b\,x^2}{3}+\frac {b^2\,x^4}{4}}{x^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 27, normalized size = 0.90 \begin {gather*} \frac {- 3 a^{2} - 8 a b x^{2} - 6 b^{2} x^{4}}{24 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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