Optimal. Leaf size=18 \[ \frac {1}{x}-3 x+\frac {x^2}{2}+3 \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {14}
\begin {gather*} \frac {x^2}{2}-3 x+\frac {1}{x}+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {-1+3 x-3 x^2+x^3}{x^2} \, dx &=\int \left (-3-\frac {1}{x^2}+\frac {3}{x}+x\right ) \, dx\\ &=\frac {1}{x}-3 x+\frac {x^2}{2}+3 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} \frac {1}{x}-3 x+\frac {x^2}{2}+3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 17, normalized size = 0.94
method | result | size |
default | \(\frac {1}{x}-3 x +\frac {x^{2}}{2}+3 \ln \left (x \right )\) | \(17\) |
risch | \(\frac {1}{x}-3 x +\frac {x^{2}}{2}+3 \ln \left (x \right )\) | \(17\) |
norman | \(\frac {1-3 x^{2}+\frac {1}{2} x^{3}}{x}+3 \ln \left (x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 16, normalized size = 0.89 \begin {gather*} \frac {1}{2} \, x^{2} - 3 \, x + \frac {1}{x} + 3 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 20, normalized size = 1.11 \begin {gather*} \frac {x^{3} - 6 \, x^{2} + 6 \, x \log \left (x\right ) + 2}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 15, normalized size = 0.83 \begin {gather*} \frac {x^{2}}{2} - 3 x + 3 \log {\left (x \right )} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.38, size = 17, normalized size = 0.94 \begin {gather*} \frac {1}{2} \, x^{2} - 3 \, x + \frac {1}{x} + 3 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 16, normalized size = 0.89 \begin {gather*} 3\,\ln \left (x\right )-3\,x+\frac {1}{x}+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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