Optimal. Leaf size=18 \[ e^{e^x x}-25 \left (-4+e^x-x\right ) \]
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Rubi [F] time = 0.10, 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 \left (25-25 e^x+e^{x+e^x x} (1+x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=25 x-25 \int e^x \, dx+\int e^{x+e^x x} (1+x) \, dx\\ &=-25 e^x+25 x+\int \left (e^{x+e^x x}+e^{x+e^x x} x\right ) \, dx\\ &=-25 e^x+25 x+\int e^{x+e^x x} \, dx+\int e^{x+e^x x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 16, normalized size = 0.89 \begin {gather*} -25 e^x+e^{e^x x}+25 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 24, normalized size = 1.33 \begin {gather*} {\left (25 \, x e^{x} + e^{\left (x e^{x} + x\right )} - 25 \, e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 13, normalized size = 0.72 \begin {gather*} 25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.78
method | result | size |
default | \(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\) | \(14\) |
norman | \(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\) | \(14\) |
risch | \(25 x +{\mathrm e}^{{\mathrm e}^{x} x}-25 \,{\mathrm e}^{x}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.72 \begin {gather*} 25 \, x + e^{\left (x e^{x}\right )} - 25 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 13, normalized size = 0.72 \begin {gather*} 25\,x+{\mathrm {e}}^{x\,{\mathrm {e}}^x}-25\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 0.78 \begin {gather*} 25 x - 25 e^{x} + e^{x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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