Optimal. Leaf size=45 \[ -\frac{2 i e^{-2 i a}}{x}-2 i e^{-3 i a} \tan ^{-1}\left (e^{-i a} x\right )+\frac{i}{3 x^3} \]
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Rubi [F] time = 0.0270119, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\tan (a+i \log (x))}{x^4} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\tan (a+i \log (x))}{x^4} \, dx &=\int \frac{\tan (a+i \log (x))}{x^4} \, dx\\ \end{align*}
Mathematica [A] time = 0.0249357, size = 70, normalized size = 1.56 \[ -\frac{2 \sin (2 a)}{x}-\frac{2 i \cos (2 a)}{x}-2 i \cos (3 a) \tan ^{-1}(x \cos (a)-i x \sin (a))-2 \sin (3 a) \tan ^{-1}(x \cos (a)-i x \sin (a))+\frac{i}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.058, size = 0, normalized size = 0. \begin{align*} \int{\frac{\tan \left ( a+i\ln \left ( x \right ) \right ) }{{x}^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.67508, size = 212, normalized size = 4.71 \begin{align*} -\frac{6 \, x^{3}{\left (-i \, \cos \left (3 \, a\right ) - \sin \left (3 \, a\right )\right )} \arctan \left (\frac{2 \, x \cos \left (a\right )}{x^{2} + \cos \left (a\right )^{2} - 2 \, x \sin \left (a\right ) + \sin \left (a\right )^{2}}, \frac{x^{2} - \cos \left (a\right )^{2} - \sin \left (a\right )^{2}}{x^{2} + \cos \left (a\right )^{2} - 2 \, x \sin \left (a\right ) + \sin \left (a\right )^{2}}\right ) + x^{3}{\left (3 \, \cos \left (3 \, a\right ) - 3 i \, \sin \left (3 \, a\right )\right )} \log \left (\frac{x^{2} + \cos \left (a\right )^{2} + 2 \, x \sin \left (a\right ) + \sin \left (a\right )^{2}}{x^{2} + \cos \left (a\right )^{2} - 2 \, x \sin \left (a\right ) + \sin \left (a\right )^{2}}\right ) + 12 \, x^{2}{\left (i \, \cos \left (2 \, a\right ) + \sin \left (2 \, a\right )\right )} - 2 i}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{-i \, e^{\left (2 i \, a - 2 \, \log \left (x\right )\right )} + i}{x^{4} e^{\left (2 i \, a - 2 \, \log \left (x\right )\right )} + x^{4}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.25665, size = 53, normalized size = 1.18 \begin{align*} \left (- \log{\left (x - i e^{i a} \right )} + \log{\left (x + i e^{i a} \right )}\right ) e^{- 3 i a} - \frac{\left (6 i x^{2} - i e^{2 i a}\right ) e^{- 2 i a}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14238, size = 38, normalized size = 0.84 \begin{align*} -2 i \, \arctan \left (x e^{\left (-i \, a\right )}\right ) e^{\left (-3 i \, a\right )} - \frac{2 i \, e^{\left (-2 i \, a\right )}}{x} + \frac{i}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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