Optimal. Leaf size=25 \[ e^{\left (3+e^{1+e^{e^{5+x}}+e^x \log (5)}\right ) x} x \]
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Rubi [B] time = 0.69, antiderivative size = 127, normalized size of antiderivative = 5.08, number of steps used = 1, number of rules used = 1, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {2288} \begin {gather*} \frac {e^{5^{e^x} e^{e^{e^{x+5}}+1} x+3 x} \left (5^{e^x} e^{e^{e^{x+5}}+1} \left (e^{x+e^{x+5}+5} x^2+e^x x^2 \log (5)+x\right )+3 x\right )}{5^{e^x} e^{e^{e^{x+5}}+1}+5^{e^x} e^{e^{e^{x+5}}+1} x \left (e^{x+e^{x+5}+5}+e^x \log (5)\right )+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{3 x+5^{e^x} e^{1+e^{e^{5+x}}} x} \left (3 x+5^{e^x} e^{1+e^{e^{5+x}}} \left (x+e^{5+e^{5+x}+x} x^2+e^x x^2 \log (5)\right )\right )}{3+5^{e^x} e^{1+e^{e^{5+x}}}+5^{e^x} e^{1+e^{e^{5+x}}} x \left (e^{5+e^{5+x}+x}+e^x \log (5)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.72, size = 25, normalized size = 1.00 \begin {gather*} e^{\left (3+5^{e^x} e^{1+e^{e^{5+x}}}\right ) x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 39, normalized size = 1.56 \begin {gather*} x e^{\left (x e^{\left ({\left (e^{\left (2 \, x + 10\right )} \log \relax (5) + e^{\left (x + e^{\left (x + 5\right )} + 10\right )} + e^{\left (x + 10\right )}\right )} e^{\left (-x - 10\right )}\right )} + 3 \, x\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*} \int {\left ({\left (x^{2} e^{x} \log \relax (5) + x^{2} e^{\left (x + e^{\left (x + 5\right )} + 5\right )} + x\right )} e^{\left (e^{x} \log \relax (5) + e^{\left (e^{\left (x + 5\right )}\right )} + 1\right )} + 3 \, x + 1\right )} e^{\left (x e^{\left (e^{x} \log \relax (5) + e^{\left (e^{\left (x + 5\right )}\right )} + 1\right )} + 3 \, x\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 21, normalized size = 0.84
method | result | size |
risch | \(x \,{\mathrm e}^{x \left (5^{{\mathrm e}^{x}} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{5+x}}+1}+3\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 22, normalized size = 0.88 \begin {gather*} x e^{\left (x e^{\left (e^{x} \log \relax (5) + e^{\left (e^{\left (x + 5\right )}\right )} + 1\right )} + 3 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.23, size = 22, normalized size = 0.88 \begin {gather*} x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{5^{{\mathrm {e}}^x}\,x\,\mathrm {e}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^5\,{\mathrm {e}}^x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 10.31, size = 26, normalized size = 1.04 \begin {gather*} x e^{x e^{e^{x} \log {\relax (5 )} + e^{e^{5} e^{x}} + 1} + 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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