Integrand size = 22, antiderivative size = 22 \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\text {Int}\left (\frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x},x\right ) \]
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Not integrable
Time = 0.14 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx \\ \end{align*}
Not integrable
Time = 0.69 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91
\[\int \frac {\operatorname {arccot}\left (c -\left (-i c +1\right ) \tan \left (b x +a \right )\right )}{x}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.64 \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\int { \frac {\operatorname {arccot}\left (-{\left (-i \, c + 1\right )} \tan \left (b x + a\right ) + c\right )}{x} \,d x } \]
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Timed out. \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\text {Timed out} \]
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Exception generated. \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\text {Exception raised: ValueError} \]
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Not integrable
Time = 1.15 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\int { \frac {\operatorname {arccot}\left (-{\left (-i \, c + 1\right )} \tan \left (b x + a\right ) + c\right )}{x} \,d x } \]
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Not integrable
Time = 1.24 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {\cot ^{-1}(c-(1-i c) \tan (a+b x))}{x} \, dx=\int \frac {\mathrm {acot}\left (c+\mathrm {tan}\left (a+b\,x\right )\,\left (-1+c\,1{}\mathrm {i}\right )\right )}{x} \,d x \]
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