Integrand size = 18, antiderivative size = 12 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \sqrt {-1+x+x^3} \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1602} \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \sqrt {x^3+x-1} \]
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Rule 1602
Rubi steps \begin{align*} \text {integral}& = 2 \sqrt {-1+x+x^3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \sqrt {-1+x+x^3} \]
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Time = 1.07 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
derivativedivides | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
default | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
trager | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
risch | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
elliptic | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
pseudoelliptic | \(2 \sqrt {x^{3}+x -1}\) | \(11\) |
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none
Time = 0.23 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \, \sqrt {x^{3} + x - 1} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \sqrt {x^{3} + x - 1} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \, \sqrt {x^{3} + x - 1} \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2 \, \sqrt {x^{3} + x - 1} \]
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Time = 4.96 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1+3 x^2}{\sqrt {-1+x+x^3}} \, dx=2\,\sqrt {x^3+x-1} \]
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