Optimal. Leaf size=20 \[ -1-59049 e^{-e^{-3+4 x}+2 x}+x \]
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Rubi [A]
time = 0.09, antiderivative size = 19, normalized size of antiderivative = 0.95, number of steps
used = 7, number of rules used = 4, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {2320, 2258,
2236, 2243} \begin {gather*} x-59049 e^{2 x-e^{4 x-3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2236
Rule 2243
Rule 2258
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+59049 \int e^{-e^{-3+4 x}+2 x} \left (-2+4 e^{-3+4 x}\right ) \, dx\\ &=x+\frac {59049}{2} \text {Subst}\left (\int e^{-\frac {x^2}{e^3}} \left (-2+\frac {4 x^2}{e^3}\right ) \, dx,x,e^{2 x}\right )\\ &=x+\frac {59049}{2} \text {Subst}\left (\int \left (-2 e^{-\frac {x^2}{e^3}}+4 e^{-3-\frac {x^2}{e^3}} x^2\right ) \, dx,x,e^{2 x}\right )\\ &=x-59049 \text {Subst}\left (\int e^{-\frac {x^2}{e^3}} \, dx,x,e^{2 x}\right )+118098 \text {Subst}\left (\int e^{-3-\frac {x^2}{e^3}} x^2 \, dx,x,e^{2 x}\right )\\ &=-59049 e^{-e^{-3+4 x}+2 x}+x-\frac {59049}{2} e^{3/2} \sqrt {\pi } \text {erf}\left (e^{-\frac {3}{2}+2 x}\right )+\left (59049 e^3\right ) \text {Subst}\left (\int e^{-3-\frac {x^2}{e^3}} \, dx,x,e^{2 x}\right )\\ &=-59049 e^{-e^{-3+4 x}+2 x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 19, normalized size = 0.95 \begin {gather*} -59049 e^{-e^{-3+4 x}+2 x}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 22, normalized size = 1.10
method | result | size |
risch | \(x -59049 \,{\mathrm e}^{-{\mathrm e}^{4 x -3}+2 x}\) | \(18\) |
default | \(x -{\mathrm e}^{-{\mathrm e}^{4 x -3}+10 \ln \left (3\right )+2 x}\) | \(22\) |
norman | \(x -{\mathrm e}^{-{\mathrm e}^{4 x -3}+10 \ln \left (3\right )+2 x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 17, normalized size = 0.85 \begin {gather*} x - 59049 \, e^{\left (2 \, x - e^{\left (4 \, x - 3\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 21, normalized size = 1.05 \begin {gather*} x - e^{\left (2 \, x - e^{\left (4 \, x - 3\right )} + 10 \, \log \left (3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 14, normalized size = 0.70 \begin {gather*} x - 59049 e^{2 x - e^{4 x - 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 21, normalized size = 1.05 \begin {gather*} x - e^{\left (2 \, x - e^{\left (4 \, x - 3\right )} + 10 \, \log \left (3\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 17, normalized size = 0.85 \begin {gather*} x-59049\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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