Optimal. Leaf size=16 \[ -\frac{1}{2 c \left (b+c x^2\right )} \]
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Rubi [A] time = 0.0093297, antiderivative size = 16, normalized size of antiderivative = 1., 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} \[ -\frac{1}{2 c \left (b+c x^2\right )} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 261
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*}
Mathematica [A] time = 0.0020596, size = 16, normalized size = 1. \[ -\frac{1}{2 c \left (b+c x^2\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,c \left ( c{x}^{2}+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970984, size = 20, normalized size = 1.25 \begin{align*} -\frac{1}{2 \,{\left (c^{2} x^{2} + b c\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40502, size = 30, normalized size = 1.88 \begin{align*} -\frac{1}{2 \,{\left (c^{2} x^{2} + b c\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.337265, size = 15, normalized size = 0.94 \begin{align*} - \frac{1}{2 b c + 2 c^{2} x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26203, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{2 \,{\left (c x^{2} + b\right )} c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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