Optimal. Leaf size=24 \[ 3+e^{e^x}+2 e^x+\frac {25}{\log (5 (4-x))} \]
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Rubi [A]
time = 0.22, antiderivative size = 23, normalized size of antiderivative = 0.96, number of steps
used = 9, number of rules used = 7, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.135, Rules used = {6820, 2320,
2225, 2437, 12, 2339, 30} \begin {gather*} e^{e^x}+2 e^x+\frac {25}{\log (5 (4-x))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2225
Rule 2320
Rule 2339
Rule 2437
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x \left (2+e^{e^x}\right )-\frac {25}{(-4+x) \log ^2(20-5 x)}\right ) \, dx\\ &=-\left (25 \int \frac {1}{(-4+x) \log ^2(20-5 x)} \, dx\right )+\int e^x \left (2+e^{e^x}\right ) \, dx\\ &=5 \text {Subst}\left (\int -\frac {5}{x \log ^2(x)} \, dx,x,20-5 x\right )+\text {Subst}\left (\int \left (2+e^x\right ) \, dx,x,e^x\right )\\ &=2 e^x-25 \text {Subst}\left (\int \frac {1}{x \log ^2(x)} \, dx,x,20-5 x\right )+\text {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=e^{e^x}+2 e^x-25 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (-5 (-4+x))\right )\\ &=e^{e^x}+2 e^x+\frac {25}{\log (5 (4-x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 21, normalized size = 0.88 \begin {gather*} e^{e^x}+2 e^x+\frac {25}{\log (-5 (-4+x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 19, normalized size = 0.79
method | result | size |
default | \(2 \,{\mathrm e}^{x}+{\mathrm e}^{{\mathrm e}^{x}}+\frac {25}{\ln \left (-5 x +20\right )}\) | \(19\) |
risch | \(2 \,{\mathrm e}^{x}+{\mathrm e}^{{\mathrm e}^{x}}+\frac {25}{\ln \left (-5 x +20\right )}\) | \(19\) |
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 [B] Leaf count of result is larger than twice the leaf count of optimal. 42 vs.
\(2 (19) = 38\).
time = 0.42, size = 42, normalized size = 1.75 \begin {gather*} \frac {{\left (2 \, e^{\left (2 \, x\right )} \log \left (-5 \, x + 20\right ) + e^{\left (x + e^{x}\right )} \log \left (-5 \, x + 20\right ) + 25 \, e^{x}\right )} e^{\left (-x\right )}}{\log \left (-5 \, x + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 17, normalized size = 0.71 \begin {gather*} 2 e^{x} + e^{e^{x}} + \frac {25}{\log {\left (20 - 5 x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 42 vs.
\(2 (19) = 38\).
time = 0.40, size = 42, normalized size = 1.75 \begin {gather*} \frac {{\left (2 \, e^{\left (2 \, x\right )} \log \left (-5 \, x + 20\right ) + e^{\left (x + e^{x}\right )} \log \left (-5 \, x + 20\right ) + 25 \, e^{x}\right )} e^{\left (-x\right )}}{\log \left (-5 \, x + 20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 18, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x}+2\,{\mathrm {e}}^x+\frac {25}{\ln \left (20-5\,x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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