Integrand size = 31, antiderivative size = 19 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=e^{x^2}+e^{4 e^x} x^6+\log (2) \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2240, 2326} \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=e^{4 e^x} x^6+e^{x^2} \]
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Rule 2240
Rule 2326
Rubi steps \begin{align*} \text {integral}& = 2 \int e^{x^2} x \, dx+\int e^{4 e^x} \left (6 x^5+4 e^x x^6\right ) \, dx \\ & = e^{x^2}+e^{4 e^x} x^6 \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=e^{x^2}+e^{4 e^x} x^6 \]
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Time = 0.53 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79
method | result | size |
default | \(x^{6} {\mathrm e}^{4 \,{\mathrm e}^{x}}+{\mathrm e}^{x^{2}}\) | \(15\) |
risch | \(x^{6} {\mathrm e}^{4 \,{\mathrm e}^{x}}+{\mathrm e}^{x^{2}}\) | \(15\) |
parallelrisch | \(x^{6} {\mathrm e}^{4 \,{\mathrm e}^{x}}+{\mathrm e}^{x^{2}}\) | \(15\) |
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=x^{6} e^{\left (4 \, e^{x}\right )} + e^{\left (x^{2}\right )} \]
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Time = 0.16 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=x^{6} e^{4 e^{x}} + e^{x^{2}} \]
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none
Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=x^{6} e^{\left (4 \, e^{x}\right )} + e^{\left (x^{2}\right )} \]
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Time = 0.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx=x^{6} e^{\left (4 \, e^{x}\right )} + e^{\left (x^{2}\right )} \]
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Time = 7.46 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (2 e^{x^2} x+e^{4 e^x} \left (6 x^5+4 e^x x^6\right )\right ) \, dx={\mathrm {e}}^{x^2}+x^6\,{\mathrm {e}}^{4\,{\mathrm {e}}^x} \]
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