Optimal. Leaf size=21 \[ \frac {1}{3} \left (\frac {3}{2}+\frac {3}{x}\right )-x+\log (2)+\log (5) \]
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Rubi [A] time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.33, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \begin {gather*} \frac {1}{x}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {1}{x^2}\right ) \, dx\\ &=\frac {1}{x}-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 0.33 \begin {gather*} \frac {1}{x}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 10, normalized size = 0.48 \begin {gather*} -\frac {x^{2} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 7, normalized size = 0.33 \begin {gather*} -x + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 8, normalized size = 0.38
method | result | size |
default | \(\frac {1}{x}-x\) | \(8\) |
risch | \(\frac {1}{x}-x\) | \(8\) |
gosper | \(-\frac {x^{2}-1}{x}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 7, normalized size = 0.33 \begin {gather*} -x + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 0.33 \begin {gather*} \frac {1}{x}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 3, normalized size = 0.14 \begin {gather*} - x + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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