Optimal. Leaf size=21 \[ \frac {e^{e^{2 (78-x+4 (3+\log (x)))}}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(21)=42\).
time = 0.05, antiderivative size = 54, normalized size of antiderivative = 2.57, number of steps
used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {2326}
\begin {gather*} \frac {e^{e^{180-2 x} x^8-2 x+180} (4-x) x^6}{4 e^{180-2 x} x^7-e^{180-2 x} x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{180-2 x+e^{180-2 x} x^8} (4-x) x^6}{4 e^{180-2 x} x^7-e^{180-2 x} x^8}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 17, normalized size = 0.81 \begin {gather*} \frac {e^{e^{180-2 x} x^8}}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 16, normalized size = 0.76
method | result | size |
norman | \(\frac {{\mathrm e}^{{\mathrm e}^{8 \ln \left (x \right )-2 x +180}}}{x}\) | \(16\) |
risch | \(\frac {{\mathrm e}^{x^{8} {\mathrm e}^{180-2 x}}}{x}\) | \(16\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 15, normalized size = 0.71 \begin {gather*} \frac {e^{\left (e^{\left (-2 \, x + 8 \, \log \left (x\right ) + 180\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 12, normalized size = 0.57 \begin {gather*} \frac {e^{x^{8} e^{180 - 2 x}}}{x} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.17, size = 15, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{x^8\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{180}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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