Optimal. Leaf size=22 \[ a x+b \log (x)-\frac {c}{x}-\frac {d}{2 x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} a x+b \log (x)-\frac {c}{x}-\frac {d}{2 x^2} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} a x+b \log (x)-\frac {c}{x}-\frac {d}{2 x^2} \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 (a+\frac {d}{x^3}+\frac {c}{x^2}+\frac {b}{x}\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.20, size = 27, normalized size = 1.23 \begin {gather*} \frac {2 \, a x^{3} + 2 \, b x^{2} \log \relax (x) - 2 \, c x - d}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 21, normalized size = 0.95 \begin {gather*} a x + b \log \left ({\left | x \right |}\right ) - \frac {c}{x} - \frac {d}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.95 \begin {gather*} a x +b \ln \relax (x )-\frac {c}{x}-\frac {d}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 20, normalized size = 0.91 \begin {gather*} a x + b \log \relax (x) - \frac {c}{x} - \frac {d}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 20, normalized size = 0.91 \begin {gather*} a\,x-\frac {\frac {d}{2}+c\,x}{x^2}+b\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 20, normalized size = 0.91 \begin {gather*} a x + b \log {\relax (x )} + \frac {- 2 c x - d}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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