Integrand size = 26, antiderivative size = 20 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=4+\left (3+e^x+x\right )^2-4 \left (10+x-16 x^4\right ) \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.50, number of steps used = 4, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2225, 2207} \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=64 x^4+x^2+2 x-2 e^x+e^{2 x}+2 e^x (x+4) \]
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Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = 2 x+x^2+64 x^4+2 \int e^{2 x} \, dx+\int e^x (8+2 x) \, dx \\ & = e^{2 x}+2 x+x^2+64 x^4+2 e^x (4+x)-2 \int e^x \, dx \\ & = -2 e^x+e^{2 x}+2 x+x^2+64 x^4+2 e^x (4+x) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.60 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=2 \left (\frac {e^{2 x}}{2}+x+\frac {x^2}{2}+32 x^4+e^x (3+x)\right ) \]
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Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25
method | result | size |
risch | \({\mathrm e}^{2 x}+\left (2 x +6\right ) {\mathrm e}^{x}+64 x^{4}+x^{2}+2 x\) | \(25\) |
default | \(64 x^{4}+2 \,{\mathrm e}^{x} x +x^{2}+{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}+2 x\) | \(26\) |
norman | \(64 x^{4}+2 \,{\mathrm e}^{x} x +x^{2}+{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}+2 x\) | \(26\) |
parallelrisch | \(64 x^{4}+2 \,{\mathrm e}^{x} x +x^{2}+{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}+2 x\) | \(26\) |
parts | \(64 x^{4}+2 \,{\mathrm e}^{x} x +x^{2}+{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}+2 x\) | \(26\) |
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none
Time = 0.22 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \]
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Time = 0.06 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=64 x^{4} + x^{2} + 2 x + \left (2 x + 6\right ) e^{x} + e^{2 x} \]
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none
Time = 0.18 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \]
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Time = 10.25 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25 \[ \int \left (2+2 e^{2 x}+2 x+256 x^3+e^x (8+2 x)\right ) \, dx=2\,x+{\mathrm {e}}^{2\,x}+6\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^x+x^2+64\,x^4 \]
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