Optimal. Leaf size=15 \[ \frac {2560000}{\left (-3+e^{e^5-4 x}\right )^2} \]
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Rubi [A]
time = 0.05, antiderivative size = 17, normalized size of antiderivative = 1.13, number of steps
used = 3, number of rules used = 3, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {12, 2320, 32}
\begin {gather*} \frac {2560000}{\left (3-e^{e^5-4 x}\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 32
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=20480000 \int \frac {e^{e^5-4 x}}{-27+e^{3 e^5-12 x}-9 e^{2 e^5-8 x}+27 e^{e^5-4 x}} \, dx\\ &=-\left (5120000 \text {Subst}\left (\int \frac {1}{(-3+x)^3} \, dx,x,e^{e^5-4 x}\right )\right )\\ &=\frac {2560000}{\left (3-e^{e^5-4 x}\right )^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 24, normalized size = 1.60 \begin {gather*} \frac {2560000 e^{8 x}}{\left (-e^{e^5}+3 e^{4 x}\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.93
method | result | size |
derivativedivides | \(\frac {2560000}{\left ({\mathrm e}^{{\mathrm e}^{5}-4 x}-3\right )^{2}}\) | \(14\) |
default | \(\frac {2560000}{\left ({\mathrm e}^{{\mathrm e}^{5}-4 x}-3\right )^{2}}\) | \(14\) |
norman | \(\frac {2560000}{\left ({\mathrm e}^{{\mathrm e}^{5}-4 x}-3\right )^{2}}\) | \(14\) |
risch | \(\frac {2560000}{\left ({\mathrm e}^{{\mathrm e}^{5}-4 x}-3\right )^{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 26, normalized size = 1.73 \begin {gather*} -\frac {2560000}{6 \, e^{\left (-4 \, x + e^{5}\right )} - e^{\left (-8 \, x + 2 \, e^{5}\right )} - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 26, normalized size = 1.73 \begin {gather*} -\frac {2560000}{6 \, e^{\left (-4 \, x + e^{5}\right )} - e^{\left (-8 \, x + 2 \, e^{5}\right )} - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 22, normalized size = 1.47 \begin {gather*} \frac {2560000}{e^{- 8 x + 2 e^{5}} - 6 e^{- 4 x + e^{5}} + 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 13, normalized size = 0.87 \begin {gather*} \frac {2560000}{{\left (e^{\left (-4 \, x + e^{5}\right )} - 3\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.17, size = 31, normalized size = 2.07 \begin {gather*} \frac {2560000\,{\mathrm {e}}^{{\mathrm {e}}^5}\,\left (6\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^{{\mathrm {e}}^5}\right )}{9\,{\left (3\,{\mathrm {e}}^{4\,x}-{\mathrm {e}}^{{\mathrm {e}}^5}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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