Optimal. Leaf size=15 \[ -\frac{1}{2 x^2}-\frac{1}{x}+\log (x) \]
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Rubi [A] time = 0.0020757, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ -\frac{1}{2 x^2}-\frac{1}{x}+\log (x) \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (\frac{1}{x^3}+\frac{1}{x^2}+\frac{1}{x}\right ) \, dx &=-\frac{1}{2 x^2}-\frac{1}{x}+\log (x)\\ \end{align*}
Mathematica [A] time = 0.0022421, size = 15, normalized size = 1. \[ -\frac{1}{2 x^2}-\frac{1}{x}+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,{x}^{2}}}-{x}^{-1}+\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.95597, size = 18, normalized size = 1.2 \begin{align*} -\frac{1}{x} - \frac{1}{2 \, x^{2}} + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94769, size = 46, normalized size = 3.07 \begin{align*} \frac{2 \, x^{2} \log \left (x\right ) - 2 \, x - 1}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080251, size = 12, normalized size = 0.8 \begin{align*} \log{\left (x \right )} - \frac{2 x + 1}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05113, size = 19, normalized size = 1.27 \begin{align*} -\frac{1}{x} - \frac{1}{2 \, x^{2}} + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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