Optimal. Leaf size=17 \[ -\frac {a}{5 x^5}-\frac {b}{7 x^7} \]
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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} \[ -\frac {a}{5 x^5}-\frac {b}{7 x^7} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{x^2}}{x^6} \, dx &=\int \left (\frac {b}{x^8}+\frac {a}{x^6}\right ) \, dx\\ &=-\frac {b}{7 x^7}-\frac {a}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {a}{5 x^5}-\frac {b}{7 x^7} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 15, normalized size = 0.88 \[ -\frac {7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 15, normalized size = 0.88 \[ -\frac {7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.82 \[ -\frac {a}{5 x^{5}}-\frac {b}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 15, normalized size = 0.88 \[ -\frac {7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.88 \[ -\frac {7\,a\,x^2+5\,b}{35\,x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 15, normalized size = 0.88 \[ \frac {- 7 a x^{2} - 5 b}{35 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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