Optimal. Leaf size=28 \[ \frac {e^{-x+\frac {e^{4 x} x}{4205}}-x}{x \log (5)} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(28)=56\).
time = 0.09, antiderivative size = 62, normalized size of antiderivative = 2.21, number of steps
used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12, 2326}
\begin {gather*} \frac {e^{\frac {e^{4 x} x-4205 x}{4205}} \left (4205 x-e^{4 x} \left (4 x^2+x\right )\right )}{x^2 \left (-4 e^{4 x} x-e^{4 x}+4205\right ) \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{\frac {-4205 x+e^{4 x} x}{4205}} \left (-4205-4205 x+e^{4 x} \left (x+4 x^2\right )\right )}{x^2} \, dx}{4205 \log (5)}\\ &=\frac {e^{\frac {-4205 x+e^{4 x} x}{4205}} \left (4205 x-e^{4 x} \left (x+4 x^2\right )\right )}{x^2 \left (4205-e^{4 x}-4 e^{4 x} x\right ) \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 23, normalized size = 0.82 \begin {gather*} \frac {e^{\left (-1+\frac {e^{4 x}}{4205}\right ) x}}{x \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 19, normalized size = 0.68
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {x \left ({\mathrm e}^{4 x}-4205\right )}{4205}}}{\ln \left (5\right ) x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 20, normalized size = 0.71 \begin {gather*} \frac {e^{\left (\frac {1}{4205} \, x e^{\left (4 \, x\right )} - x\right )}}{x \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 20, normalized size = 0.71 \begin {gather*} \frac {e^{\left (\frac {1}{4205} \, x e^{\left (4 \, x\right )} - x\right )}}{x \log \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 15, normalized size = 0.54 \begin {gather*} \frac {e^{\frac {x e^{4 x}}{4205} - x}}{x \log {\left (5 \right )}} \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 = 1.03, size = 20, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{4\,x}}{4205}}}{x\,\ln \left (5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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