Optimal. Leaf size=15 \[ e^{6 \left (e^{-x}-5 x\right )}+x \]
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Rubi [A] time = 0.16, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {6742, 2282, 2288} \begin {gather*} x+e^{6 e^{-x}-30 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2282
Rule 2288
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-6 e^{6 e^{-x}-31 x} \left (1+5 e^x\right )\right ) \, dx\\ &=x-6 \int e^{6 e^{-x}-31 x} \left (1+5 e^x\right ) \, dx\\ &=x-6 \operatorname {Subst}\left (\int \frac {e^{6/x} (1+5 x)}{x^{32}} \, dx,x,e^x\right )\\ &=e^{6 e^{-x}-30 x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 15, normalized size = 1.00 \begin {gather*} e^{6 \left (e^{-x}-5 x\right )}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 16, normalized size = 1.07 \begin {gather*} x + e^{\left (-6 \, {\left (5 \, x e^{x} - 1\right )} e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.87 \begin {gather*} x + e^{\left (-30 \, x + 6 \, e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 1.00
method | result | size |
default | \(x +{\mathrm e}^{6 \,{\mathrm e}^{-x}} {\mathrm e}^{-30 x}\) | \(15\) |
risch | \({\mathrm e}^{-6 \left (5 \,{\mathrm e}^{x} x -1\right ) {\mathrm e}^{-x}}+x\) | \(17\) |
norman | \(\left ({\mathrm e}^{x} x +{\mathrm e}^{x} {\mathrm e}^{2 \left (-15 \,{\mathrm e}^{x} x +3\right ) {\mathrm e}^{-x}}\right ) {\mathrm e}^{-x}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 13, normalized size = 0.87 \begin {gather*} x + e^{\left (-30 \, x + 6 \, e^{\left (-x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.54, size = 13, normalized size = 0.87 \begin {gather*} x+{\mathrm {e}}^{6\,{\mathrm {e}}^{-x}-30\,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 = 0.93 \begin {gather*} x + e^{2 \left (- 15 x e^{x} + 3\right ) e^{- x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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