Optimal. Leaf size=23 \[ \frac {5+i \pi +\log (4)}{x+e^{5+e^5} x} \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 3, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6, 12, 30} \begin {gather*} \frac {5+i \pi +\log (4)}{\left (1+e^{5+e^5}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-5-i \pi -\log (4)}{\left (1+e^{5+e^5}\right ) x^2} \, dx\\ &=-\frac {(5+i \pi +\log (4)) \int \frac {1}{x^2} \, dx}{1+e^{5+e^5}}\\ &=\frac {5+i \pi +\log (4)}{\left (1+e^{5+e^5}\right ) x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.04 \begin {gather*} \frac {5+i \pi +\log (4)}{\left (1+e^{5+e^5}\right ) x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 21, normalized size = 0.91 \begin {gather*} \frac {i \, \pi + 2 \, \log \relax (2) + 5}{x e^{\left (e^{5} + 5\right )} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 22, normalized size = 0.96 \begin {gather*} \frac {i \, \pi + 2 \, \log \relax (2) + 5}{x {\left (e^{\left (e^{5} + 5\right )} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 25, normalized size = 1.09
method | result | size |
gosper | \(\frac {2 \ln \relax (2)+i \pi +5}{{\mathrm e}^{\ln \relax (x )+{\mathrm e}^{5}} {\mathrm e}^{5}+x}\) | \(25\) |
default | \(-\frac {-2 \ln \relax (2)-i \pi -5}{\left ({\mathrm e}^{{\mathrm e}^{5}+5}+1\right ) x}\) | \(25\) |
norman | \(\frac {2 \ln \relax (2)+i \pi +5}{\left ({\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{5}}+1\right ) x}\) | \(25\) |
risch | \(\frac {i \pi }{\left ({\mathrm e}^{{\mathrm e}^{5}+5}+1\right ) x}+\frac {2 \ln \relax (2)}{\left ({\mathrm e}^{{\mathrm e}^{5}+5}+1\right ) x}+\frac {5}{\left ({\mathrm e}^{{\mathrm e}^{5}+5}+1\right ) x}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 23, normalized size = 1.00 \begin {gather*} -\frac {-i \, \pi - 2 \, \log \relax (2) - 5}{x {\left (e^{\left (e^{5} + 5\right )} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 21, normalized size = 0.91 \begin {gather*} \frac {\ln \relax (4)+5+\Pi \,1{}\mathrm {i}}{x\,\left ({\mathrm {e}}^{{\mathrm {e}}^5+5}+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 24, normalized size = 1.04 \begin {gather*} - \frac {2 \log {\relax (2 )} + 5 + i \pi }{x \left (- e^{5} e^{e^{5}} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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