Integrand size = 25, antiderivative size = 22 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=20 \left (25+e^5+x-\left (5-e^{1+x}+x\right )^2\right ) \]
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Time = 0.01 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.59, number of steps used = 4, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {2225, 2207} \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=-20 x^2-180 x-40 e^{x+1}-20 e^{2 x+2}+40 e^{x+1} (x+6) \]
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Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = -180 x-20 x^2-40 \int e^{2+2 x} \, dx+\int e^{1+x} (240+40 x) \, dx \\ & = -20 e^{2+2 x}-180 x-20 x^2+40 e^{1+x} (6+x)-40 \int e^{1+x} \, dx \\ & = -40 e^{1+x}-20 e^{2+2 x}-180 x-20 x^2+40 e^{1+x} (6+x) \\ \end{align*}
Time = 0.09 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.45 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=20 \left (-e^{2+2 x}-9 x-x^2+2 e^x (5 e+e x)\right ) \]
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Time = 0.20 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.27
method | result | size |
risch | \(-20 \,{\mathrm e}^{2+2 x}+\left (200+40 x \right ) {\mathrm e}^{1+x}-20 x^{2}-180 x\) | \(28\) |
norman | \(40 x \,{\mathrm e}^{1+x}-20 x^{2}+200 \,{\mathrm e}^{1+x}-20 \,{\mathrm e}^{2+2 x}-180 x\) | \(31\) |
parallelrisch | \(40 x \,{\mathrm e}^{1+x}-20 x^{2}+200 \,{\mathrm e}^{1+x}-20 \,{\mathrm e}^{2+2 x}-180 x\) | \(31\) |
default | \(-180 x +40 \,{\mathrm e}^{1+x} \left (1+x \right )+160 \,{\mathrm e}^{1+x}-20 x^{2}-20 \,{\mathrm e}^{2+2 x}\) | \(33\) |
parts | \(-180 x +40 \,{\mathrm e}^{1+x} \left (1+x \right )+160 \,{\mathrm e}^{1+x}-20 x^{2}-20 \,{\mathrm e}^{2+2 x}\) | \(33\) |
derivativedivides | \(-140-140 x +40 \,{\mathrm e}^{1+x} \left (1+x \right )+160 \,{\mathrm e}^{1+x}-20 \left (1+x \right )^{2}-20 \,{\mathrm e}^{2+2 x}\) | \(36\) |
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Time = 0.27 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=-20 \, x^{2} + 40 \, {\left (x + 5\right )} e^{\left (x + 1\right )} - 180 \, x - 20 \, e^{\left (2 \, x + 2\right )} \]
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Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=- 20 x^{2} - 180 x + \left (40 x + 200\right ) e^{x + 1} - 20 e^{2 x + 2} \]
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Time = 0.18 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=-20 \, x^{2} + 40 \, {\left (x e + 5 \, e\right )} e^{x} - 180 \, x - 20 \, e^{\left (2 \, x + 2\right )} \]
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Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=-20 \, x^{2} + 40 \, {\left (x + 5\right )} e^{\left (x + 1\right )} - 180 \, x - 20 \, e^{\left (2 \, x + 2\right )} \]
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Time = 14.49 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \left (-180-40 e^{2+2 x}-40 x+e^{1+x} (240+40 x)\right ) \, dx=200\,{\mathrm {e}}^{x+1}-180\,x-20\,{\mathrm {e}}^{2\,x+2}+40\,x\,{\mathrm {e}}^{x+1}-20\,x^2 \]
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