Integrand size = 16, antiderivative size = 18 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {1}{3} \left (1-e^{5/3}-x\right )^2 \]
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Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {9} \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {1}{3} \left (-x-e^{5/3}+1\right )^2 \]
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Rule 9
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \left (1-e^{5/3}-x\right )^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {2}{3} \left (-x+e^{5/3} x+\frac {x^2}{2}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.61
method | result | size |
gosper | \(\frac {x \left (x +2 \,{\mathrm e}^{\frac {5}{3}}-2\right )}{3}\) | \(11\) |
default | \(\frac {2 x \,{\mathrm e}^{\frac {5}{3}}}{3}+\frac {x^{2}}{3}-\frac {2 x}{3}\) | \(15\) |
norman | \(\left (\frac {2 \,{\mathrm e}^{\frac {5}{3}}}{3}-\frac {2}{3}\right ) x +\frac {x^{2}}{3}\) | \(15\) |
risch | \(\frac {2 x \,{\mathrm e}^{\frac {5}{3}}}{3}+\frac {x^{2}}{3}-\frac {2 x}{3}\) | \(15\) |
parallelrisch | \(\left (\frac {2 \,{\mathrm e}^{\frac {5}{3}}}{3}-\frac {2}{3}\right ) x +\frac {x^{2}}{3}\) | \(15\) |
parts | \(\frac {2 x \,{\mathrm e}^{\frac {5}{3}}}{3}+\frac {x^{2}}{3}-\frac {2 x}{3}\) | \(15\) |
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none
Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {1}{3} \, x^{2} + \frac {2}{3} \, x e^{\frac {5}{3}} - \frac {2}{3} \, x \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {x^{2}}{3} + x \left (- \frac {2}{3} + \frac {2 e^{\frac {5}{3}}}{3}\right ) \]
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none
Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {1}{3} \, x^{2} + \frac {2}{3} \, x e^{\frac {5}{3}} - \frac {2}{3} \, x \]
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none
Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {1}{3} \, x^{2} + \frac {2}{3} \, x e^{\frac {5}{3}} - \frac {2}{3} \, x \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.56 \[ \int \frac {1}{3} \left (-2+2 e^{5/3}+2 x\right ) \, dx=\frac {x\,\left (x+2\,{\mathrm {e}}^{5/3}-2\right )}{3} \]
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