Optimal. Leaf size=21 \[ \frac {x}{(2+x) \log (x (-5+i \pi +\log (3)))} \]
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Rubi [F] time = 0.20, 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 {-2-x+2 \log (-5 x+x (i \pi +\log (3)))}{\left (4+4 x+x^2\right ) \log ^2(-5 x+x (i \pi +\log (3)))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2-x+2 \log (-5 x+x (i \pi +\log (3)))}{(2+x)^2 \log ^2(-5 x+x (i \pi +\log (3)))} \, dx\\ &=\int \frac {-2-x+2 \log (-5 x+x (i \pi +\log (3)))}{(2+x)^2 \log ^2(-x (5-i \pi -\log (3)))} \, dx\\ &=\int \left (\frac {1}{(-2-x) \log ^2(-x (5-i \pi -\log (3)))}+\frac {2}{(2+x)^2 \log (-x (5-i \pi -\log (3)))}\right ) \, dx\\ &=2 \int \frac {1}{(2+x)^2 \log (x (-5+i \pi +\log (3)))} \, dx+\int \frac {1}{(-2-x) \log ^2(x (-5+i \pi +\log (3)))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 21, normalized size = 1.00 \begin {gather*} \frac {x}{(2+x) \log (x (-5+i \pi +\log (3)))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 22, normalized size = 1.05 \begin {gather*} \frac {x}{{\left (x + 2\right )} \log \left ({\left (i \, \pi - 5\right )} x + x \log \relax (3)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 35, normalized size = 1.67 \begin {gather*} \frac {x}{x \log \left (i \, \pi x + x \log \relax (3) - 5 \, x\right ) + 2 \, \log \left (i \, \pi x + x \log \relax (3) - 5 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.43, size = 24, normalized size = 1.14
method | result | size |
norman | \(\frac {x}{\left (2+x \right ) \ln \left (x \left (\ln \relax (3)+i \pi \right )-5 x \right )}\) | \(24\) |
risch | \(\frac {x}{\left (2+x \right ) \ln \left (x \left (\ln \relax (3)+i \pi \right )-5 x \right )}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 31, normalized size = 1.48 \begin {gather*} \frac {x}{x \log \left (i \, \pi + \log \relax (3) - 5\right ) + {\left (x + 2\right )} \log \relax (x) + 2 \, \log \left (i \, \pi + \log \relax (3) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.82, size = 20, normalized size = 0.95 \begin {gather*} \frac {x}{\ln \left (x\,\left (\ln \relax (3)-5+\Pi \,1{}\mathrm {i}\right )\right )\,\left (x+2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 0.90 \begin {gather*} \frac {x}{\left (x + 2\right ) \log {\left (- 5 x + x \log {\relax (3 )} + i \pi x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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