Optimal. Leaf size=20 \[ x (-e+x) \left (-4+e^x+3 (-5+x) x^3\right ) \]
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Rubi [B] time = 0.06, antiderivative size = 54, normalized size of antiderivative = 2.70, number of steps used = 11, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2196, 2176, 2194} \begin {gather*} 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) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \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 {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 23, normalized size = 1.15 \begin {gather*} -\left ((e-x) x \left (-4+e^x-15 x^3+3 x^4\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.76, size = 46, normalized size = 2.30 \begin {gather*} 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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 47, normalized size = 2.35 \begin {gather*} 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 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.03, size = 47, normalized size = 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 | \(\left (-x \,{\mathrm e}+x^{2}\right ) {\mathrm e}^{x}-3 x^{5} {\mathrm e}+15 x^{4} {\mathrm e}+4 x \,{\mathrm e}+3 x^{6}-15 x^{5}-4 x^{2}\) | \(48\) |
default | \({\mathrm e}^{x} x^{2}-{\mathrm e} \,{\mathrm e}^{x}-{\mathrm e} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+{\mathrm e} \left (-3 x^{5}+15 x^{4}+4 x \right )-4 x^{2}-15 x^{5}+3 x^{6}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 46, normalized size = 2.30 \begin {gather*} 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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 22, normalized size = 1.10 \begin {gather*} x\,\left (x-\mathrm {e}\right )\,\left ({\mathrm {e}}^x-15\,x^3+3\,x^4-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 48, normalized size = 2.40 \begin {gather*} 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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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