Optimal. Leaf size=13 \[ c \log (x)-\frac{b}{2 x^2} \]
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Rubi [A] time = 0.00563, antiderivative size = 13, normalized size of antiderivative = 1., 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} \[ c \log (x)-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{b x^2+c x^4}{x^5} \, dx &=\int \left (\frac{b}{x^3}+\frac{c}{x}\right ) \, dx\\ &=-\frac{b}{2 x^2}+c \log (x)\\ \end{align*}
Mathematica [A] time = 0.0023213, size = 13, normalized size = 1. \[ c \log (x)-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 12, normalized size = 0.9 \begin{align*} -{\frac{b}{2\,{x}^{2}}}+c\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03018, size = 19, normalized size = 1.46 \begin{align*} \frac{1}{2} \, c \log \left (x^{2}\right ) - \frac{b}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25098, size = 41, normalized size = 3.15 \begin{align*} \frac{2 \, c x^{2} \log \left (x\right ) - b}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.290268, size = 10, normalized size = 0.77 \begin{align*} - \frac{b}{2 x^{2}} + c \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25866, size = 27, normalized size = 2.08 \begin{align*} \frac{1}{2} \, c \log \left (x^{2}\right ) - \frac{c x^{2} + b}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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