Optimal. Leaf size=17 \[ -\frac {a}{8 x^8}-\frac {b}{4 x^4} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ -\frac {a}{8 x^8}-\frac {b}{4 x^4} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^9} \, dx &=\int \left (\frac {a}{x^9}+\frac {b}{x^5}\right ) \, dx\\ &=-\frac {a}{8 x^8}-\frac {b}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {a}{8 x^8}-\frac {b}{4 x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 13, normalized size = 0.76 \[ -\frac {2 \, b x^{4} + a}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.76 \[ -\frac {2 \, b x^{4} + a}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ -\frac {b}{4 x^{4}}-\frac {a}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 13, normalized size = 0.76 \[ -\frac {2 \, b x^{4} + a}{8 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.76 \[ -\frac {2\,b\,x^4+a}{8\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 14, normalized size = 0.82 \[ \frac {- a - 2 b x^{4}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
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