Optimal. Leaf size=29 \[ 2 i e^{-i a} \tan ^{-1}\left (e^{-i a} x\right )+\frac{i}{x} \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.0277522, 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 = {} \[ \int \frac{\tan (a+i \log (x))}{x^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\tan (a+i \log (x))}{x^2} \, dx &=\int \frac{\tan (a+i \log (x))}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 0.0238917, size = 44, normalized size = 1.52 \[ 2 i \cos (a) \tan ^{-1}(x \cos (a)-i x \sin (a))+2 \sin (a) \tan ^{-1}(x \cos (a)-i x \sin (a))+\frac{i}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.059, size = 0, normalized size = 0. \begin{align*} \int{\frac{\tan \left ( a+i\ln \left ( x \right ) \right ) }{{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 1.63297, size = 171, normalized size = 5.9 \begin{align*} \frac{2 \, x{\left (-i \, \cos \left (a\right ) - \sin \left (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{\left (\cos \left (a\right ) - i \, \sin \left (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 ) + 2 i}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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^{2} e^{\left (2 i \, a - 2 \, \log \left (x\right )\right )} + x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.456843, size = 27, normalized size = 0.93 \begin{align*} \left (\log{\left (x - i e^{i a} \right )} - \log{\left (x + i e^{i a} \right )}\right ) e^{- i a} + \frac{i}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17649, size = 38, normalized size = 1.31 \begin{align*} -\frac{2 \, \arctan \left (\frac{i \, x}{\sqrt{-e^{\left (2 i \, a\right )}}}\right )}{\sqrt{-e^{\left (2 i \, a\right )}}} + \frac{i}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]