Optimal. Leaf size=17 \[ -\frac {a}{7 x^7}-\frac {b}{3 x^3} \]
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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} \[ -\frac {a}{7 x^7}-\frac {b}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^8} \, dx &=\int \left (\frac {a}{x^8}+\frac {b}{x^4}\right ) \, dx\\ &=-\frac {a}{7 x^7}-\frac {b}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {a}{7 x^7}-\frac {b}{3 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 15, normalized size = 0.88 \[ -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.88 \[ -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]
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 \[ -\frac {b}{3 x^{3}}-\frac {a}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 15, normalized size = 0.88 \[ -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \]
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 \[ -\frac {7\,b\,x^4+3\,a}{21\,x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 15, normalized size = 0.88 \[ \frac {- 3 a - 7 b x^{4}}{21 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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