Optimal. Leaf size=25 \[ -\frac {a}{7 x^7}-\frac {b}{5 x^5}-\frac {c}{3 x^3} \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14} \[ -\frac {a}{7 x^7}-\frac {b}{5 x^5}-\frac {c}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2+c x^4}{x^8} \, dx &=\int \left (\frac {a}{x^8}+\frac {b}{x^6}+\frac {c}{x^4}\right ) \, dx\\ &=-\frac {a}{7 x^7}-\frac {b}{5 x^5}-\frac {c}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \[ -\frac {a}{7 x^7}-\frac {b}{5 x^5}-\frac {c}{3 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.40, size = 21, normalized size = 0.84 \[ -\frac {35 \, c x^{4} + 21 \, b x^{2} + 15 \, a}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 21, normalized size = 0.84 \[ -\frac {35 \, c x^{4} + 21 \, b x^{2} + 15 \, a}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 0.80 \[ -\frac {c}{3 x^{3}}-\frac {b}{5 x^{5}}-\frac {a}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 21, normalized size = 0.84 \[ -\frac {35 \, c x^{4} + 21 \, b x^{2} + 15 \, a}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 21, normalized size = 0.84 \[ -\frac {\frac {c\,x^4}{3}+\frac {b\,x^2}{5}+\frac {a}{7}}{x^7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 22, normalized size = 0.88 \[ \frac {- 15 a - 21 b x^{2} - 35 c x^{4}}{105 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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