Integrand size = 46, antiderivative size = 20 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=x (-e+x) \left (-4+e^x+3 (-5+x) x^3\right ) \]
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Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(20)=40\).
Time = 0.04 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.70, number of steps used = 11, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2227, 2207, 2225} \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=3 x^6-3 e x^5-15 x^5+15 e x^4+e^x x^2-4 x^2+4 e x+e^{x+1}-e^{x+1} (x+1) \]
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Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = -4 x^2-15 x^5+3 x^6+e \int \left (4+60 x^3-15 x^4\right ) \, dx+\int e^x \left (e (-1-x)+2 x+x^2\right ) \, dx \\ & = 4 e x-4 x^2+15 e x^4-15 x^5-3 e x^5+3 x^6+\int \left (2 e^x x+e^x x^2-e^{1+x} (1+x)\right ) \, dx \\ & = 4 e x-4 x^2+15 e x^4-15 x^5-3 e x^5+3 x^6+2 \int e^x x \, dx+\int e^x x^2 \, dx-\int e^{1+x} (1+x) \, dx \\ & = 4 e x+2 e^x x-4 x^2+e^x x^2+15 e x^4-15 x^5-3 e x^5+3 x^6-e^{1+x} (1+x)-2 \int e^x \, dx-2 \int e^x x \, dx+\int e^{1+x} \, dx \\ & = -2 e^x+e^{1+x}+4 e x-4 x^2+e^x x^2+15 e x^4-15 x^5-3 e x^5+3 x^6-e^{1+x} (1+x)+2 \int e^x \, dx \\ & = e^{1+x}+4 e x-4 x^2+e^x x^2+15 e x^4-15 x^5-3 e x^5+3 x^6-e^{1+x} (1+x) \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=-\left ((e-x) x \left (-4+e^x-15 x^3+3 x^4\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(46\) vs. \(2(20)=40\).
Time = 0.36 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.35
method | result | size |
norman | \(\left (-3 \,{\mathrm e}-15\right ) x^{5}+{\mathrm e}^{x} x^{2}-4 x^{2}+3 x^{6}+4 x \,{\mathrm e}+15 x^{4} {\mathrm e}-x \,{\mathrm e} \,{\mathrm e}^{x}\) | \(47\) |
risch | \(-3 x^{5} {\mathrm e}+3 x^{6}+15 x^{4} {\mathrm e}-15 x^{5}-x \,{\mathrm e}^{1+x}+{\mathrm e}^{x} x^{2}+4 x \,{\mathrm e}-4 x^{2}\) | \(49\) |
parallelrisch | \(-3 x^{5} {\mathrm e}+3 x^{6}+15 x^{4} {\mathrm e}-15 x^{5}-x \,{\mathrm e} \,{\mathrm e}^{x}+{\mathrm e}^{x} x^{2}+4 x \,{\mathrm e}-4 x^{2}\) | \(49\) |
default | \({\mathrm e}^{x} x^{2}-{\mathrm e} \,{\mathrm e}^{x}-{\mathrm e} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+{\mathrm e} \left (-3 x^{5}+15 x^{4}+4 x \right )-4 x^{2}-15 x^{5}+3 x^{6}\) | \(59\) |
parts | \({\mathrm e}^{x} x^{2}-{\mathrm e} \,{\mathrm e}^{x}-{\mathrm e} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-4 x^{2}-15 x^{5}+3 x^{6}+15 x^{4} {\mathrm e}-3 x^{5} {\mathrm e}+4 x \,{\mathrm e}\) | \(61\) |
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.30 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=3 \, x^{6} - 15 \, x^{5} - 4 \, x^{2} - {\left (3 \, x^{5} - 15 \, x^{4} - 4 \, x\right )} e + {\left (x^{2} - x e\right )} e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (19) = 38\).
Time = 0.05 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.40 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=3 x^{6} + x^{5} \left (-15 - 3 e\right ) + 15 e x^{4} - 4 x^{2} + 4 e x + \left (x^{2} - e x\right ) e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (20) = 40\).
Time = 0.19 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.30 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=3 \, x^{6} - 15 \, x^{5} - 4 \, x^{2} - {\left (3 \, x^{5} - 15 \, x^{4} - 4 \, x\right )} e + {\left (x^{2} - x e\right )} e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 47 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.35 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=3 \, x^{6} - 15 \, x^{5} + x^{2} e^{x} - 4 \, x^{2} - {\left (3 \, x^{5} - 15 \, x^{4} - 4 \, x\right )} e - x e^{\left (x + 1\right )} \]
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Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \left (-8 x-75 x^4+18 x^5+e^x \left (e (-1-x)+2 x+x^2\right )+e \left (4+60 x^3-15 x^4\right )\right ) \, dx=x\,\left (x-\mathrm {e}\right )\,\left ({\mathrm {e}}^x-15\,x^3+3\,x^4-4\right ) \]
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