Integrand size = 22, antiderivative size = 12 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^2}{2 \sqrt {a}} \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {2, 12, 30} \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^2}{2 \sqrt {a}} \]
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Rule 2
Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{\sqrt {a}} \, dx \\ & = \frac {\int x \, dx}{\sqrt {a}} \\ & = \frac {x^2}{2 \sqrt {a}} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^2}{2 \sqrt {a}} \]
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Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
gosper | \(\frac {x^{2}}{2 \sqrt {a}}\) | \(9\) |
default | \(\frac {x^{2}}{2 \sqrt {a}}\) | \(9\) |
norman | \(\frac {x^{2}}{2 \sqrt {a}}\) | \(9\) |
parallelrisch | \(\frac {x^{2}}{2 \sqrt {a}}\) | \(9\) |
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none
Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^{2}}{2 \, \sqrt {a}} \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^{2}}{2 \sqrt {a}} \]
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none
Time = 0.18 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^{2}}{2 \, \sqrt {a}} \]
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none
Time = 0.28 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^{2}}{2 \, \sqrt {a}} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {x}{\sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx=\frac {x^2}{2\,\sqrt {a}} \]
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