Optimal. Leaf size=23 \[ -x+10 e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x \]
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Rubi [F] time = 1.83, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{9} e^{\frac {1}{9} \left (-4 x-4 e^{4+3 x} x\right )} \left (90-9 e^{\frac {1}{9} \left (4 x+4 e^{4+3 x} x\right )}-40 x+e^{4+3 x} \left (-40 x-120 x^2\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int e^{\frac {1}{9} \left (-4 x-4 e^{4+3 x} x\right )} \left (90-9 e^{\frac {1}{9} \left (4 x+4 e^{4+3 x} x\right )}-40 x+e^{4+3 x} \left (-40 x-120 x^2\right )\right ) \, dx\\ &=\frac {1}{9} \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} \left (90-9 e^{\frac {1}{9} \left (4 x+4 e^{4+3 x} x\right )}-40 x+e^{4+3 x} \left (-40 x-120 x^2\right )\right ) \, dx\\ &=\frac {1}{9} \int \left (-9+90 e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x}-40 e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x-40 e^{4+3 x-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x (1+3 x)\right ) \, dx\\ &=-x-\frac {40}{9} \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x \, dx-\frac {40}{9} \int e^{4+3 x-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x (1+3 x) \, dx+10 \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} \, dx\\ &=-x-\frac {40}{9} \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x \, dx-\frac {40}{9} \int e^{\frac {1}{9} \left (36+23 x-4 e^{4+3 x} x\right )} x (1+3 x) \, dx+10 \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} \, dx\\ &=-x-\frac {40}{9} \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x \, dx-\frac {40}{9} \int \left (e^{\frac {1}{9} \left (36+23 x-4 e^{4+3 x} x\right )} x+3 e^{\frac {1}{9} \left (36+23 x-4 e^{4+3 x} x\right )} x^2\right ) \, dx+10 \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} \, dx\\ &=-x-\frac {40}{9} \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} x \, dx-\frac {40}{9} \int e^{\frac {1}{9} \left (36+23 x-4 e^{4+3 x} x\right )} x \, dx+10 \int e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x} \, dx-\frac {40}{3} \int e^{\frac {1}{9} \left (36+23 x-4 e^{4+3 x} x\right )} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.77, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{9} \left (-9+90 e^{-\frac {4}{9} \left (1+e^{4+3 x}\right ) x}\right ) x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 36, normalized size = 1.57 \begin {gather*} -{\left (x e^{\left (\frac {4}{9} \, x e^{\left (3 \, x + 4\right )} + \frac {4}{9} \, x\right )} - 10 \, x\right )} e^{\left (-\frac {4}{9} \, x e^{\left (3 \, x + 4\right )} - \frac {4}{9} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {1}{9} \, {\left (40 \, {\left (3 \, x^{2} + x\right )} e^{\left (3 \, x + 4\right )} + 40 \, x + 9 \, e^{\left (\frac {4}{9} \, x e^{\left (3 \, x + 4\right )} + \frac {4}{9} \, x\right )} - 90\right )} e^{\left (-\frac {4}{9} \, x e^{\left (3 \, x + 4\right )} - \frac {4}{9} \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 20, normalized size = 0.87
method | result | size |
risch | \(-x +10 x \,{\mathrm e}^{-\frac {4 x \left ({\mathrm e}^{4+3 x}+1\right )}{9}}\) | \(20\) |
norman | \(\left (10 x -x \,{\mathrm e}^{\frac {4 x \,{\mathrm e}^{4+3 x}}{9}+\frac {4 x}{9}}\right ) {\mathrm e}^{-\frac {4 x \,{\mathrm e}^{4+3 x}}{9}-\frac {4 x}{9}}\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -x - \frac {1}{9} \, \int 10 \, {\left (4 \, {\left (3 \, x^{2} e^{4} + x e^{4}\right )} e^{\left (3 \, x\right )} + 4 \, x - 9\right )} e^{\left (-\frac {4}{9} \, x e^{\left (3 \, x + 4\right )} - \frac {4}{9} \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.12, size = 21, normalized size = 0.91 \begin {gather*} 10\,x\,{\mathrm {e}}^{-\frac {4\,x}{9}-\frac {4\,x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4}{9}}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 24, normalized size = 1.04 \begin {gather*} 10 x e^{- \frac {4 x e^{3 x + 4}}{9} - \frac {4 x}{9}} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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