Optimal. Leaf size=17 \[ -\frac {b}{5 x^5}-\frac {c}{3 x^3} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \begin {gather*} -\frac {b}{5 x^5}-\frac {c}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^8} \, dx &=\int \left (\frac {b}{x^6}+\frac {c}{x^4}\right ) \, dx\\ &=-\frac {b}{5 x^5}-\frac {c}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {b}{5 x^5}-\frac {c}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {b x^2+c x^4}{x^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.54, size = 15, normalized size = 0.88 \begin {gather*} -\frac {5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.88 \begin {gather*} -\frac {5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \end {gather*}
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 \begin {gather*} -\frac {c}{3 x^{3}}-\frac {b}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 15, normalized size = 0.88 \begin {gather*} -\frac {5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \end {gather*}
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 \begin {gather*} -\frac {5\,c\,x^2+3\,b}{15\,x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 15, normalized size = 0.88 \begin {gather*} \frac {- 3 b - 5 c x^{2}}{15 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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