Optimal. Leaf size=30 \[ -\frac {a^2}{9 x^9}-\frac {2 a b}{7 x^7}-\frac {b^2}{5 x^5} \]
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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} \[ -\frac {a^2}{9 x^9}-\frac {2 a b}{7 x^7}-\frac {b^2}{5 x^5} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^2}{x^{10}} \, dx &=\int \left (\frac {a^2}{x^{10}}+\frac {2 a b}{x^8}+\frac {b^2}{x^6}\right ) \, dx\\ &=-\frac {a^2}{9 x^9}-\frac {2 a b}{7 x^7}-\frac {b^2}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ -\frac {a^2}{9 x^9}-\frac {2 a b}{7 x^7}-\frac {b^2}{5 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 26, normalized size = 0.87 \[ -\frac {63 \, b^{2} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 26, normalized size = 0.87 \[ -\frac {63 \, b^{2} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \[ -\frac {b^{2}}{5 x^{5}}-\frac {2 a b}{7 x^{7}}-\frac {a^{2}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 26, normalized size = 0.87 \[ -\frac {63 \, b^{2} x^{4} + 90 \, a b x^{2} + 35 \, a^{2}}{315 \, x^{9}} \]
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 \[ -\frac {\frac {a^2}{9}+\frac {2\,a\,b\,x^2}{7}+\frac {b^2\,x^4}{5}}{x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 27, normalized size = 0.90 \[ \frac {- 35 a^{2} - 90 a b x^{2} - 63 b^{2} x^{4}}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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