Optimal. Leaf size=16 \[ -\frac {1}{2 c \left (b+c x^2\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1584, 261} \begin {gather*} -\frac {1}{2 c \left (b+c x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rule 1584
Rubi steps
\begin {align*} \int \frac {x^5}{\left (b x^2+c x^4\right )^2} \, dx &=\int \frac {x}{\left (b+c x^2\right )^2} \, dx\\ &=-\frac {1}{2 c \left (b+c x^2\right )}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{2 c \left (b+c x^2\right )} \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 {x^5}{\left (b x^2+c x^4\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.62, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{2 \, {\left (c^{2} x^{2} + b c\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{2 \, {\left (c x^{2} + b\right )} c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{2 \left (c \,x^{2}+b \right ) c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 15, normalized size = 0.94 \begin {gather*} -\frac {1}{2 \, {\left (c^{2} x^{2} + b c\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{2\,c\,\left (c\,x^2+b\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 15, normalized size = 0.94 \begin {gather*} - \frac {1}{2 b c + 2 c^{2} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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