Integrand size = 14, antiderivative size = 20 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=2-3 \left (3-\frac {1}{2 x}-x+\log ^2(4)\right ) \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.55, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=3 x+\frac {3}{2 x} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \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{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.55 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=\frac {3}{2 x}+3 x \]
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Time = 0.09 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.50
method | result | size |
default | \(\frac {3}{2 x}+3 x\) | \(10\) |
risch | \(\frac {3}{2 x}+3 x\) | \(10\) |
norman | \(\frac {\frac {3}{2}+3 x^{2}}{x}\) | \(12\) |
gosper | \(\frac {\frac {3}{2}+3 x^{2}}{x}\) | \(13\) |
parallelrisch | \(\frac {6 x^{2}+3}{2 x}\) | \(13\) |
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Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=\frac {3 \, {\left (2 \, x^{2} + 1\right )}}{2 \, x} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.35 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=3 x + \frac {3}{2 x} \]
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none
Time = 0.22 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=3 \, x + \frac {3}{2 \, x} \]
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Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=3 \, x + \frac {3}{2 \, x} \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.45 \[ \int \frac {-3+6 x^2}{2 x^2} \, dx=3\,x+\frac {3}{2\,x} \]
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