Optimal. Leaf size=15 \[ \frac{x^2}{2}-\frac{1}{x}+\log (x) \]
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Rubi [A] time = 0.0035479, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {14} \[ \frac{x^2}{2}-\frac{1}{x}+\log (x) \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{1+x+x^3}{x^2} \, dx &=\int \left (\frac{1}{x^2}+\frac{1}{x}+x\right ) \, dx\\ &=-\frac{1}{x}+\frac{x^2}{2}+\log (x)\\ \end{align*}
Mathematica [A] time = 0.0007965, size = 15, normalized size = 1. \[ \frac{x^2}{2}-\frac{1}{x}+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 14, normalized size = 0.9 \begin{align*} -{x}^{-1}+{\frac{{x}^{2}}{2}}+\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09369, size = 18, normalized size = 1.2 \begin{align*} \frac{1}{2} \, x^{2} - \frac{1}{x} + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20762, size = 41, normalized size = 2.73 \begin{align*} \frac{x^{3} + 2 \, x \log \left (x\right ) - 2}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070176, size = 10, normalized size = 0.67 \begin{align*} \frac{x^{2}}{2} + \log{\left (x \right )} - \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14995, size = 19, normalized size = 1.27 \begin{align*} \frac{1}{2} \, x^{2} - \frac{1}{x} + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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