Optimal. Leaf size=22 \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
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Rubi [A] time = 0.0039866, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+\frac{d}{x^3}+\frac{c}{x^2}+\frac{b}{x}\right ) \, dx &=-\frac{d}{2 x^2}-\frac{c}{x}+a x+b \log (x)\\ \end{align*}
Mathematica [A] time = 0.0063733, size = 22, normalized size = 1. \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 21, normalized size = 1. \begin{align*} -{\frac{d}{2\,{x}^{2}}}-{\frac{c}{x}}+ax+b\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983506, size = 27, normalized size = 1.23 \begin{align*} a x + b \log \left (x\right ) - \frac{c}{x} - \frac{d}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.0407, size = 65, normalized size = 2.95 \begin{align*} \frac{2 \, a x^{3} + 2 \, b x^{2} \log \left (x\right ) - 2 \, c x - d}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.305357, size = 19, normalized size = 0.86 \begin{align*} a x + b \log{\left (x \right )} - \frac{2 c x + d}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07752, size = 28, normalized size = 1.27 \begin{align*} a x + b \log \left ({\left | x \right |}\right ) - \frac{c}{x} - \frac{d}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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