Optimal. Leaf size=30 \[ \frac {(i \pi +\log (2))^2}{x^2 \left (-5+e^{e^3 \left (e^x+x\right )}+x\right )^2} \]
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Rubi [A] time = 1.25, antiderivative size = 35, normalized size of antiderivative = 1.17, number of steps used = 3, number of rules used = 3, integrand size = 169, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6688, 12, 6687} \begin {gather*} -\frac {(\pi -i \log (2))^2}{\left (-x-e^{e^3 \left (x+e^x\right )}+5\right )^2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6687
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (5-e^{e^3 \left (e^x+x\right )}-2 x-e^{3+e^{3+x}+e^3 x} x-e^{3+e^{3+x}+x+e^3 x} x\right ) (\pi -i \log (2))^2}{\left (5-e^{e^3 \left (e^x+x\right )}-x\right )^3 x^3} \, dx\\ &=\left (2 (\pi -i \log (2))^2\right ) \int \frac {5-e^{e^3 \left (e^x+x\right )}-2 x-e^{3+e^{3+x}+e^3 x} x-e^{3+e^{3+x}+x+e^3 x} x}{\left (5-e^{e^3 \left (e^x+x\right )}-x\right )^3 x^3} \, dx\\ &=-\frac {(\pi -i \log (2))^2}{\left (5-e^{e^3 \left (e^x+x\right )}-x\right )^2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.85, size = 33, normalized size = 1.10 \begin {gather*} -\frac {(\pi -i \log (2))^2}{x^2 \left (-5+e^{e^{3+x}+e^3 x}+x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.59, size = 71, normalized size = 2.37 \begin {gather*} -\frac {\pi ^{2} - 2 i \, \pi \log \relax (2) - \log \relax (2)^{2}}{x^{4} - 10 \, x^{3} + x^{2} e^{\left (2 \, x e^{3} + 2 \, e^{\left (x + 3\right )}\right )} + 25 \, x^{2} + 2 \, {\left (x^{3} - 5 \, x^{2}\right )} e^{\left (x e^{3} + e^{\left (x + 3\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.49, size = 80, normalized size = 2.67 \begin {gather*} -\frac {\pi ^{2} - 2 i \, \pi \log \relax (2) - \log \relax (2)^{2}}{x^{4} + 2 \, x^{3} e^{\left (x e^{3} + e^{\left (x + 3\right )}\right )} - 10 \, x^{3} + x^{2} e^{\left (2 \, x e^{3} + 2 \, e^{\left (x + 3\right )}\right )} - 10 \, x^{2} e^{\left (x e^{3} + e^{\left (x + 3\right )}\right )} + 25 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 37, normalized size = 1.23
method | result | size |
risch | \(-\frac {-2 i \pi \ln \relax (2)+\pi ^{2}-\ln \relax (2)^{2}}{x^{2} \left ({\mathrm e}^{{\mathrm e}^{3+x}+x \,{\mathrm e}^{3}}+x -5\right )^{2}}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 4.19, size = 71, normalized size = 2.37 \begin {gather*} -\frac {\pi ^{2} - 2 i \, \pi \log \relax (2) - \log \relax (2)^{2}}{x^{4} - 10 \, x^{3} + x^{2} e^{\left (2 \, x e^{3} + 2 \, e^{\left (x + 3\right )}\right )} + 25 \, x^{2} + 2 \, {\left (x^{3} - 5 \, x^{2}\right )} e^{\left (x e^{3} + e^{\left (x + 3\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^{x\,{\mathrm {e}}^3+{\mathrm {e}}^3\,{\mathrm {e}}^x}\,\left ({\left (\ln \relax (2)+\Pi \,1{}\mathrm {i}\right )}^2\,\left (2\,x\,{\mathrm {e}}^3+2\right )+2\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\,{\left (\ln \relax (2)+\Pi \,1{}\mathrm {i}\right )}^2\right )+\left (4\,x-10\right )\,{\left (\ln \relax (2)+\Pi \,1{}\mathrm {i}\right )}^2}{{\mathrm {e}}^{x\,{\mathrm {e}}^3+{\mathrm {e}}^3\,{\mathrm {e}}^x}\,\left (3\,x^5-30\,x^4+75\,x^3\right )-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^3+2\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,\left (15\,x^3-3\,x^4\right )-125\,x^3+75\,x^4-15\,x^5+x^6+x^3\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^3+3\,{\mathrm {e}}^3\,{\mathrm {e}}^x}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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