Integrand size = 10, antiderivative size = 10 \[ \int \frac {\tan (a+b x)}{x} \, dx=\text {Int}\left (\frac {\tan (a+b x)}{x},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\tan (a+b x)}{x} \, dx=\int \frac {\tan (a+b x)}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\tan (a+b x)}{x} \, dx \\ \end{align*}
Not integrable
Time = 1.55 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int \frac {\tan (a+b x)}{x} \, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00
\[\int \frac {\tan \left (b x +a \right )}{x}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int { \frac {\tan \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.32 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int \frac {\tan {\left (a + b x \right )}}{x}\, dx \]
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Not integrable
Time = 0.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int { \frac {\tan \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 0.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int { \frac {\tan \left (b x + a\right )}{x} \,d x } \]
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Not integrable
Time = 3.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\tan (a+b x)}{x} \, dx=\int \frac {\mathrm {tan}\left (a+b\,x\right )}{x} \,d x \]
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