Integrand size = 18, antiderivative size = 14 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {1}{2} x^2 \left (e^{4/3}+x\right ) \]
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Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {x^3}{2}+\frac {1}{2} e^{4/3} x^2 \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \left (2 e^{4/3} x+3 x^2\right ) \, dx \\ & = \frac {1}{2} e^{4/3} x^2+\frac {x^3}{2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.43 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {1}{2} e^{4/3} x^2+\frac {x^3}{2} \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71
method | result | size |
gosper | \(\frac {\left (x +{\mathrm e}^{\frac {4}{3}}\right ) x^{2}}{2}\) | \(10\) |
default | \(\frac {x^{3}}{2}+\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}\) | \(14\) |
norman | \(\frac {x^{3}}{2}+\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}\) | \(14\) |
risch | \(\frac {x^{3}}{2}+\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}\) | \(14\) |
parallelrisch | \(\frac {x^{3}}{2}+\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}\) | \(14\) |
parts | \(\frac {x^{3}}{2}+\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}\) | \(14\) |
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Time = 0.23 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {x^{3}}{2} + \frac {x^{2} e^{\frac {4}{3}}}{2} \]
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Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \]
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Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \]
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Time = 12.71 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {1}{2} \left (2 e^{4/3} x+3 x^2\right ) \, dx=\frac {x^2\,\left (x+{\mathrm {e}}^{4/3}\right )}{2} \]
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