Optimal. Leaf size=15 \[ -\frac {a}{5 x^5}-\frac {b}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 15, 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} \[ -\frac {a}{5 x^5}-\frac {b}{x} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^6} \, dx &=\int \left (\frac {a}{x^6}+\frac {b}{x^2}\right ) \, dx\\ &=-\frac {a}{5 x^5}-\frac {b}{x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {a}{5 x^5}-\frac {b}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 13, normalized size = 0.87 \[ -\frac {5 \, b x^{4} + a}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.87 \[ -\frac {5 \, b x^{4} + a}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \[ -\frac {b}{x}-\frac {a}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 13, normalized size = 0.87 \[ -\frac {5 \, b x^{4} + a}{5 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.87 \[ -\frac {5\,b\,x^4+a}{5\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 14, normalized size = 0.93 \[ \frac {- a - 5 b x^{4}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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