Optimal. Leaf size=15 \[ -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {1}{2 x^2}-\frac {1}{x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (\frac {1}{x^3}+\frac {1}{x^2}+\frac {1}{x}\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.23, size = 17, normalized size = 1.13 \begin {gather*} \frac {2 \, x^{2} \log \relax (x) - 2 \, x - 1}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 14, normalized size = 0.93 \begin {gather*} -\frac {1}{x} - \frac {1}{2 \, x^{2}} + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} \ln \relax (x )-\frac {1}{x}-\frac {1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.04, size = 13, normalized size = 0.87 \begin {gather*} -\frac {1}{x} - \frac {1}{2 \, x^{2}} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.73 \begin {gather*} \ln \relax (x)-\frac {x+\frac {1}{2}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.93 \begin {gather*} \log {\relax (x )} + \frac {- 2 x - 1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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