Optimal. Leaf size=20 \[ 2-3 \left (3-\frac {1}{2 x}-x+\log ^2(4)\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.55, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \begin {gather*} 3 x+\frac {3}{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {-3+6 x^2}{x^2} \, dx\\ &=\frac {1}{2} \int \left (6-\frac {3}{x^2}\right ) \, dx\\ &=\frac {3}{2 x}+3 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.55 \begin {gather*} \frac {3}{2 x}+3 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 12, normalized size = 0.60 \begin {gather*} \frac {3 \, {\left (2 \, x^{2} + 1\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 9, normalized size = 0.45 \begin {gather*} 3 \, x + \frac {3}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 10, normalized size = 0.50
method | result | size |
default | \(3 x +\frac {3}{2 x}\) | \(10\) |
risch | \(3 x +\frac {3}{2 x}\) | \(10\) |
norman | \(\frac {\frac {3}{2}+3 x^{2}}{x}\) | \(12\) |
gosper | \(\frac {\frac {3}{2}+3 x^{2}}{x}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 9, normalized size = 0.45 \begin {gather*} 3 \, x + \frac {3}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.45 \begin {gather*} 3\,x+\frac {3}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 7, normalized size = 0.35 \begin {gather*} 3 x + \frac {3}{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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