Optimal. Leaf size=25 \[ \frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^2} \]
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Rubi [F]
time = 3.18, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \left (2 e^{5+e^x+3 x}+(-2+x) \log (x)+e^{5+e^x+3 x} \left (3 x+e^x x\right ) \log (x) \log \left (\log ^2(x)\right )\right )}{x^3 \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} (-2+x)}{x^3}+\frac {e^{9+e^x+5 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2}+\frac {e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \left (2+3 x \log (x) \log \left (\log ^2(x)\right )\right )}{x^3 \log (x)}\right ) \, dx\\ &=\int \frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} (-2+x)}{x^3} \, dx+\int \frac {e^{9+e^x+5 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2} \, dx+\int \frac {e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \left (2+3 x \log (x) \log \left (\log ^2(x)\right )\right )}{x^3 \log (x)} \, dx\\ &=\int \left (-\frac {2 e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^3}+\frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^2}\right ) \, dx+\int \frac {e^{9+e^x+5 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2} \, dx+\int \left (\frac {2 e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^3 \log (x)}+\frac {3 e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^3} \, dx\right )+2 \int \frac {e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^3 \log (x)} \, dx+3 \int \frac {e^{9+e^x+4 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2} \, dx+\int \frac {e^{4+x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )}}{x^2} \, dx+\int \frac {e^{9+e^x+5 x+e^{5+e^x+3 x} \log \left (\log ^2(x)\right )} \log \left (\log ^2(x)\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.41, size = 24, normalized size = 0.96 \begin {gather*} \frac {e^{4+x} \log ^2(x)^{e^{5+e^x+3 x}}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 3.48, size = 100, normalized size = 4.00
method | result | size |
risch | \(\frac {\ln \left (x \right )^{2 \,{\mathrm e}^{{\mathrm e}^{x}+3 x +5}} {\mathrm e}^{4-\frac {i {\mathrm e}^{{\mathrm e}^{x}+3 x +5} \pi \mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )^{3}}{2}+i {\mathrm e}^{{\mathrm e}^{x}+3 x +5} \pi \mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \left (x \right )\right )-\frac {i {\mathrm e}^{{\mathrm e}^{x}+3 x +5} \pi \,\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right ) \mathrm {csgn}\left (i \ln \left (x \right )\right )^{2}}{2}+x}}{x^{2}}\) | \(100\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 21, normalized size = 0.84 \begin {gather*} \frac {e^{\left (2 \, e^{\left (3 \, x + e^{x} + 5\right )} \log \left (\log \left (x\right )\right ) + x + 4\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 22, normalized size = 0.88 \begin {gather*} \frac {e^{\left (e^{\left (3 \, x + e^{x} + 5\right )} \log \left (\log \left (x\right )^{2}\right ) + x + 4\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.24, size = 24, normalized size = 0.96 \begin {gather*} \frac {e^{x + e^{3 x + e^{x} + 5} \log {\left (\log {\left (x \right )}^{2} \right )} + 4}}{x^{2}} \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 = 5.50, size = 23, normalized size = 0.92 \begin {gather*} \frac {{\mathrm {e}}^4\,{\mathrm {e}}^x\,{\left ({\ln \left (x\right )}^2\right )}^{{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^5}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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