Integrand size = 13, antiderivative size = 16 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=x^2+\frac {\sqrt {2} x^3}{3} \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {\sqrt {2} x^3}{3}+x^2 \]
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Rubi steps \begin{align*} \text {integral}& = x^2+\frac {\sqrt {2} x^3}{3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=x^2+\frac {\sqrt {2} x^3}{3} \]
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Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.81
method | result | size |
norman | \(x^{2}+\frac {x^{3} \sqrt {2}}{3}\) | \(13\) |
risch | \(x^{2}+\frac {x^{3} \sqrt {2}}{3}\) | \(13\) |
parallelrisch | \(x^{2}+\frac {x^{3} \sqrt {2}}{3}\) | \(13\) |
parts | \(x^{2}+\frac {x^{3} \sqrt {2}}{3}\) | \(13\) |
default | \(\sqrt {2}\, \left (\frac {x^{3}}{3}+\frac {x^{2} \sqrt {2}}{2}\right )\) | \(19\) |
gosper | \(\frac {x^{2} \left (2 x +3 \sqrt {2}\right ) \left (x \sqrt {2}+2\right )}{6 x +6 \sqrt {2}}\) | \(29\) |
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Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {\sqrt {2} x^{3}}{3} + x^{2} \]
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Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \]
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Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {1}{3} \, \sqrt {2} x^{3} + x^{2} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \left (2 x+\sqrt {2} x^2\right ) \, dx=\frac {x^2\,\left (\sqrt {2}\,x+3\right )}{3} \]
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